Concept of Volleyball - Free Essay Example

Sample details Pages: 8 Words: 2271 Downloads: 7 Date added: 2019/04/02 Category Sports Essay Level High school Tags: Volleyball Essay Did you like this example? Sports fill the nation with diehard fans and hours of television screen times for many people daily. For some sports though there are many rules, regulations, and dynamics behind the game. For instance, volleyball is a game many are fans of, but many who have never seen a match or have a head of volleyball alone may find the game confusing. Don’t waste time! Our writers will create an original "Concept of Volleyball" essay for you Create order Through the decades volleyball is a sport that has changed drastically. Changing the concepts of ruling and regulations of the game. Rules for high school matches versus club matches. The dynamics of getting the perfect pass or mastering that serves to ace the opponent. All in all, volleyball is commonly known as the most underrated and unappreciated sport of our generation. Having this mindset diminishes the key concepts of volleyball. The idea of the game with the equipment, terms, fundamentals and the rules of the game. The idea of volleyball begins with two teams with six players on each side. The players use their hands to take a ball back and forth over a regulated high net. The ball must touch the court within the opponents playing area before it can be returned. To prevent this a player on the opposing team gets the ball up and toward a teammate, before it touches the court surface†that teammate may then volley it back across the net or guide it to a third teammate who volleys it across the net. A team is allowed only three touches of the ball at a minimum before it must be returned over the net to the other team. A touch is regulated as any physical contact with the ball. Rather it is with the players hand, or head a touch is a touch. There are ruling with touching the ball also. For instance, if a player contacts the ball trying to catch it and throw it back up this would be ruled as a lift. In this instance, the call by the ref would be made and the ball and point would be given to the other team. Volleyball requires a minimum of equipment and space and can be played indoors or outdoors. The game is played on a smooth-surfaced court, divided by a center line into two equal areas, one of which is selected by or assigned to each of the two teams. Players may not step completely beyond the center line while the ball is in play. A tightly stretched net is placed across the court exactly above the middle of the center line. The height of the net and the antennas are all regulated to correctly admit to the age of the players. A ball must pass over the net entirely between the antennae. In this sport, there are allowed 6 players on each side at a time. Normally, you would have your libero, setters, hitters, and back ro w players. Volleyball has three common terms used when having the ball getting at most three touches on it before it is sent back over to the opposing team. Volleyball has changed into a very specialized sport. Many teams will include in their starting line-up a setter, two center blockers, two receiver-hitters, and a universal spiker. Only certain players will be involved with service reception. Players will also have specialist positions for attack and defense. Substitutions are allowed during the game. Since 1998, volleyball has been using a new scoring system. Teams scored a point on every rally, meaning a rally point system. Regardless of which team served. Formerly, a team could only win a point if it served the ball. Winning the serve back from the opposition was known as a side-out. Matches are played best of five sets. The first four sets are played to 25 points, with the final set being played to 15 points. A team must win a set by two points. There is no ceiling, so a set continues until one of the teams gains a two-point advantage. Previously, all sets were to 15 points, with the first four sets having a ceiling of 17 and the final set requiring at least a two-point winning advantage (fivb.org). First, there is a pass. When a player passes a ball, their forearms are straight and at a 90-degree angle from their body. Their hands are either in a cuffed fist or flat prayer hands common terms used for the positioning of the players hands for passing. Many believe that the best way for passing is staying low at a 90-degree angle that can have the passes at a neutral position that makes it easier to contact the ball. The best passers seem to move backward, absorbing the ball on their arms allowing for more control passing. Also, the way the players body is positioned during a pass is very important too. The angle of their forearms has positioned the speed of the ball, and the position of their feet. These three concepts depend on the angle and the height of the ball being passed to the setter. In the end, making the setters job easier. Libero is most commonly the best passer on a team. They are the player who wears the different colored jersey indicating special subs or rotations that wouldnt normally be allowed with a normal colored jersey. The liberos base or home for plays is normally on the far left side of the 10-foot line. There they are expected to dig balls from the right side, middle or outside hitters to keep the ball in play. Liberos are most commonly the most agile and quickest on their feet. Liberos are known for picking up balls that are far above their head or to diving from their base to the 10-foot line to keep the ball in play. Most commonly if the setter happens to take the first ball the libero is expected to take the second contact to set up the hitter for an attack. The libero always must keep their head on a swivel. Being a libero though has many regulations. They can only serve once, they must substitute behind the 10-foot line, they cannot pass the 10-foot line on an attack and they cannot set a ball that is in front of the 10-foot line either. Along with the Libero, there are also the back-row players. These are the ones who are most likely designated for passing and getting the ball to the setter and making it easier for the setter to get the ball to the hitters. These three contacts or less make it difficult for the other team to receive or try to get up. Back row players are commonly forgotten when a great hit or set came to be. There wouldnt have been a rally in the first place. Most back row players are loud and agile and wanting to get to every ball and making it known who has the ball. For instance, when a back-row player is going to become in contact with the ball most players say mine. Indicating that they are going to contact the ball and having others ready for the next contact. Not only does the back row come with fundamentals it is very important to always have their head on a swivel. If the setter messes up the ball, they try their best to better the ball and get it over. Also, when a hitter is going to conta ct the ball the back-row player can communicate to them where to hit it. The line is straight down the court vertically, or cross hitting the ball diagonally. Other key terms for indicating to the hitter to hit but seeing how important it is for the back-row player to fully communicate. Next, is setting. Wide hands and fingers are placed above the eye level and forehead level of the player. Using both their arms and legs, the player pushes the ball with both of their hands at the same time to set the ball. The setter is commonly the captain of the team meaning they oversee the plays and keeping the rest of the players in line. Setters must know the lineup and certain rotations and communicating shots and certain tactics to get a point for their team. The setters need to beat the ball to the spot and being ready to anticipation the location of the pass. Also, be ready to move from their base in case of a miss pass or miss communication between the passers and get in position to set. The setters are the one who is to set up the hitters for their attacks. Setters must have good hands and eye-hand coordination for getting the balls from the passers and to the hitters for an attack. Being a setter is a very important task. They oversee telling their hitters what they are hitting or what plays they are running. For example, is the outside going to hit a fast set, known as a 4, or are they going to come in hitting a higher ball in the middle, known as a 2? Setters oversee also communicating with not only their hitters but their back-row players also. They need to communicate to them that they need a higher pass or a tighter pass to the net to keep them on. With all the accountabilities of a setter, there are many advantages too. Setters contact the ball 95% of the time. They are most likely the teams captain or all-around player depending on their atheism and accountability. Lastly, the most common term is hitting. While hitting one either does the standing approach or the jumping approach. Either way, the player starts out with their hands in front of their body in an almost runners position. As the ball is set up and realized from the setters hand, they would take their dominant hand behind their head at another 90-degree angle and use the other hand as a glider of the ball. Now, with a jumping approach, as the set ball hits its peak, you would start the approach. As a dominant right-handed person, one would start with their left foot stepping forward, then right and then jump on their left to contact the ball. Withstanding or jump hitting, one would contact the ball with the center of their palm as fast as they could sending the ball across the end. All in all, in getting three contacts. Bump, set, spike or pas s, set, hit. Hitters are the teams key assets normally to finishing a rally. They are the ones with will most likely send the ball over with an aggressive attack on the other team. Having three hitters in the front row is the most common way to play. Hitting starts out with a strong hand and forearm, high vertical, and strong finish. When hitting one must start with their hand above their head at a 90-degree angle facing upward. After this, the ball is tossed to the hitter. When contact is made the ball should touch the palm of their hand with their fingers spread out. Once contact is made, the player needs to follow through. What this means is that the players hand and forearm should swing all the way through to where the hand should be facing downward, and having the ball go over the net at a fast and hard speed. The concept of hitting comes along with a term called blocking. This is when a hitter on the other side of the attacker is jumping up to interfere with the attackers hit. Blocking is an action that a player or players close to the net to intercept the ball coming from the opponent by reaching higher than the top of the net (theartofcoachingvolleyball.com). Only front-row players are allowed to complete a block. A block is completed whenever the ball is touched by a blocker. A collective block is acted by two or three players close to each other. In blocking, the player may place their hands and arms anywhere above the net, provided that this action does not interfere with the opponents hit or the net. Now if the player does touch the net or interferes with the pursuit of the players hit the ref will blow their whistle and give the point to the attacking team. All the terms and uses of volleyball can get confusing, but there are limitations and regulations as well. Each team may request a maximum of two time-outs and six substitutions per set. The request for time-outs or substitutions must be made after the play has ended. A coach is not allowed to sub or ask for a time-out mid-play. A team is not allowed to make multiple requests for substitution during the same interruption (theartofcoachingvolleyball.com). Two or more players can be substituted at the same time within the same request. Regular game interruptions may be requested by the coach, or in the absence of the coach, by the game captain, and only by them. Substitution before the start of a set is permitted and should be recorded as a regular substitution in that set. The ideas of volleyball along with the equipment, terms, fundamentals and the rules of the game, it shows many how a sport has so much more than what meets the eye. For example, finding more facts that people havent heard or even seen before. Volleyball is not only a physical but mental sport as well. With all the skills and teamwork, a certain team can have. A truly good team has a connection and c ommitment to the sport many seem to push away. Works Cited 35th FIVB Congress 2016. Official Volleyball Rules 2017-2020. FIVB-Vo

Drug Alcohol And Its Effects - 2128 Words

An elderly man, Frank went to his doctor for a routine check up after having some complications with his heart. While at the doctor, he was encouraged that having an alcoholic beverage a day to lower his risk of heart disease. After much consideration about the doctors prescription Frank decides with his wife that it may be a good idea. Frank had never drank before in his life, and what this doctor suggests will be a huge factor in him. Frank became an alcoholic at the age of 72. This brings questions to mind such as if Frank had been educated about alcohol and its effects of it in over abundance, would this have changed his outcome? People become responsible by being properly taught, given responsibility, and then held accountable for†¦show more content†¦Most states after the prohibition set their legal drinking age to 21 which at the time was the age of majority at the time. Few states had a lower purchase age for alcohol. Thirty states followed these minority states in the early 1970 s; of which the majority lowered the MLDA to 18 years of age (Wagenaar A. C., 1993). Most states reasoning behind this lowering of this age of majority was because the legal voting age was changed from 21 to 18 in 1971. With continued moment through the years things altered each states though and reasoning and again a majority change the alcohol purchase age to 19 years of age. The bump in age was because of an increase of 18 year old deaths and alcohol related accidents (Wagenaar A. C., 1993). There were also direct correlations to the seat belt laws and these numbers. In 1984 congress passed a law requiring states to raise their legal ages of purchase to 21 by Oct of 1986 or loose funding for their federal highways. By mid-1988, all 50 states and the District of Columbia had raised their purchase ages to 21 (Wagenaar A. C., 1993). With the drinking age at 21 and higher than the legal age of majority, brings some tension for many Americans. Alcohol has been an issue for many ages, even in biblical times there were issues with alcohol and drunkenness. The United States current solution, that of negligence and head s in the sand, is not working. The laws that there are for the minimum legal drinking age or MLDA are not

The Mind-Body Problem free essay sample

He believed in an independent soul inhabiting in a mechanically operated body. The reality of the body needed no proof, but the reality of the soul did. Since he doubted everything, he said that we could not doubt the existence of our self, because there must be a self that exists to do the doubting. Descartes was concerned about how the nonmaterial soul could interact with the matter of our body. He resolved the problem of the incompatibility of the two entities by naming this problem dualism. Dualism is an ancient concept and is deeply rooted in Greek thought. They said that a persons soul was of an entirely different essence than the body. They also said that those dual entities had no interaction with one another. They saw them as foreign to one another; the body was the prison house of the soul. In the problem of dualism, Descartes discussed that the body could be divided up, such as removing a hand or a leg, but the soul was indivisible. The soul occupied the whole body, and the removal of any part of the physical body did not reduce any part of the soul. He claims the body was procreated, and the soul was created. Even though the two realities of the soul were of a completely different character, they could react with each other. He finds that reaction as a mystery. The interdependence of the mind and body was what Descartes considered a human being. The mind and body formed a unit. Descartes said that the body, including the brain, was simply mechanical in its principal of operation. That is only true if the body is considered without a soul. The mechanistic view of the brain was not questionable if the soul doesnt make any essential part of its operation. Descartes talked about the nature of the soul, since it has no matter or substance. He said that the perceptions of sense and physical passions of people are dependent upon the body, but the awareness lies within the soul. The soul become aware, such as conscious and self consciousness, and how it succeeds in acting upon the body. Its awareness is due to the action of the body upon it. Descartes said that the body is just extended matter, and the soul is unextended spirit. When the extended is acted upon by the unextended, a definite point of interaction is required, and is found in a place in the brain called the pineal gland. The point of interaction was at the site of the pineal gland, and it was the only place he thought that is not duplicate as all other brain structures were thought to be. He said the soul wasnt to be viewed as locked in and shut up in the pineal gland. He said it was just the point of interaction, but not the box of the soul in any sense. The soul is united to all parts of the body conjointly. The whole body is the souls housing as long as the body remains intact. When a part of the body is cut off, such as a leg or finger, there is no loss of part of the soul as a consequence because the soul is indivisible. It just occupies what is left of the body. Descartes clearly stated there is a dualism of the mind and body, and their interaction is very real. Our brain is the major place for the consciousness of the soul, yet consciousness is distributed throughout the whole body. Descartes made the mind and brain separate entities, dependent upon each other. I thought of an analogy to go with that; a fountain pen and ink. They are interdependent, and the pen will not write without the ink, and the ink carries no message without the pen. I strongly believe in the idea of dualism that Descartes proposed. The mental and physical have quite different properties. Mental events have a subjective quality to them, where physical events seem not to. An example would be when one asks what a burned finger feels like, or what nice music sounds. Sensations like these cannot be reduced to something physical. There is no place in the brain where electric stimulation can cause a person to believe or decide. Although our thoughts can be true or false, our brains status cannot be true or false. Nobody can tell what we are thinking by measuring brain waves. What really grounded my position on arguing for Descartes position was the doubting argument; I can doubt that my body exists, but I cannot doubt that I exist as a thinking thing because I am existing to think. I also think that Descartes argument is true because of his idea about the soul being an indivisible, nonphysical entity. Just because someone loses their legs in a car accident, it doesnt mean their soul goes away with their lost legs. People who criticize and oppose Descartes ideas claim that if the soul and body were substances of entirely different natures, interaction between them would be impossible. Duality means that there are there are two types of substances in the world, physical and non physical. There needs to be another substance to rationalize having a brain and having a god, and free will. If the brain is performing physical duties to make us think, then wheres my soul? How am I involved in making decisions and thinking? There must be something apart from this brain and physical world. Another argument is also based upon what happens if the brain is damaged. When damage occurs from physical trauma or pathological diseases, our mental powers are always compromised. The argument holds that if the brain and mind were actually separate, our mental powers would not be compromised. It is a very strong opposing argument, however, it also depends upon the presumption that God does not have a reason for letting our brain limit our mental function while we are living. The arguments for the existence of dualism are strong, but they are dependent upon an anti-supernatural presumption. Descartes mind-body problem is definitely an open ended topic with strong arguments from the supporting or opposing side. Its a very interesting and intriguing topic. It all started with his quote about the ability to exist within his thoughts, I think, therefore I am. I believe that the body and mind/soul are two completely different parts that make a unit of the human being. They intertwine and interact in a very mysterious way. The idea of dualism was further continued and researched by many other famous philosophers such as Thomas Nagel. This is something that will rest in my thoughts more, as I continue to ponder about the nature of my soul, the interaction it has with my body, and my existence.

Kamdhenu Case free essay sample

DECISION ANALYSIS CASE STUDY Kamdhenu Case GROUP 5 Abhijeet Mahajan Amit Vijay Bishakha Majumdar Gaurav Khatri Sahil Sambyal Sakshi Makkar Vaibhav Rastogi Introduction: The Kamdhenu Dairy is a cooperative of the dairy farmers – located in Sanand, a small town in one of the western states of India. Set up with a goal to ensure a steady market and revenue for the small dairy farmers, the Kamdhenu Dairy supplies pasteurized milk to the State Government – in a fixed quantity (75000 litres/day), throughout the year. However, the production of milk has wide seasonal variations – with production of milk in winter being 250 % of that in summer. The additional milk is used for producing other milk products. The problems before the KD are as follows: 1. Finding the optimum product mix. 2. Deciding if they should continue with the loss making products – cheese and baby food. Question 1: Should Cheese be dropped from the product line ass suggested by Mr. We will write a custom essay sample on Kamdhenu Case or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Ramaswamy? Answer: After the analysis, as is clearly visible from the value of the shadow price of the Cheese, it’s both positive and large than the values of other products. Hence, we should continue with the production of cheese. Microsoft Excel 14. 0 Sensitivity Report| | | | | | Worksheet: [DA Kamdhenu. lsx]Sheet2| | | | | | Report Created: 8/26/2011 3:52:39 AM| | | | | | | | | | | | | | | | | | | | | | Variable Cells| | | | | | | Â  | Â  | Final| Reduced| Objective| Allowable| Allowable| | Cell| Name| Value| Cost| Coefficient| Increase| Decrease| | $B$18| Solution x1| 7. 5957| 0| 503| 407| 55| | $C$18| Solution x2| 0| -55| 448| 55| 1E+30| | $D$18| Solution x3| 0| -366| 544| 366| 1E+30| | $E$18| Solution x4| 0| -555| 355| 555| 1E+30| | $F$18| Solution x5| 2. 4743| 0| 910| 923| 45| | $G$18| Solution x6| 0| -165| 745| 165| 1E+30| | $H$18| Solution x7| 0| -45| 865| 45| 1E+30| | $I$18| Solution x8| 0| -277| 633| 277| 1E+30| $J$18| Solution x9| 1. 83| 0| 1833| 1E+30| 223| | $K$18| Solution x10| 0| -223| 1610| 223| 1E+30| | $L$18| Solution x11| 0| -151| 759| 151| 1E+30| | $M$18| Solution x12| 0| -278| 632| 278| 1E+30| | | | | | | | | Constraints| | | | | | | Â  | Â  | Final| Shadow| Constraint| Allowable| Allowable| | Cell| Name| Value| Price| R. H. Side| Increase| Decrease| | $N$10| Cheese Constraint Total| 1. 83| 923| 1. 83| 2. 4743| 1. 83| | $N$11| Raw Milk Procurement Total| 11. 9| 910| 11. 9| 2. 615355172| 2. 4743| | $N$12| FA Milk Govt Supply Total| 7. 5957| -407| 7. 5957| 2. 4743| 2. 615355172| | $N$6| Butter Constraint Total| 2. 951592| 0| 10| 1E+30| 7. 0048408| | $N$7| Ghee Constraint Total| 0| 0| 2. 5| 1E+30| 2. 5| | $N$8| Milk Powder Constraint Total| 3. 587735| 0| 7. 38| 1E+30| 3. 792265| | $N$9| Baby Food Constraint Total| 0| 0| 5. 36| 1E+30| 5. 36| x1| x2| x3| x4| x5| x6| x7| x8| x9| x10| x11| x12| FA Milk + Butter| FA Milk + Ghee| SMP + Butter| SMP + Ghee| WMP + Butter| WMP + Ghee| Baby Food + Butter| Baby Food + Ghee| Cheese + Butter| Cheese + Ghee| SM + Butter| SM + Ghee| Question 2: What should be the production program for the Dairy if it had no contractual obligations to supply FA Milk to the State Milk Scheme? Answer1: The production scheme for both the summer as well as the winter months can be found out from the two tables by just looking at the final values. For Summer Months (May to August) Microsoft Excel 14. 0 Sensitivity Report| | | | | | Worksheet: [DA Kamdhenu. xlsx]Sheet2| | | | | | Report Created: 8/26/2011 11:46:17 AM| | | | | | | | | | | | | | | | | | | | | | Variable Cells| | | | | | | Â  | Â  | Final| Reduced| Objective| Allowable| Allowable| | Cell| Name| Value| Cost| Coefficient| Increase| Decrease| | $B$18| Solution x1| 0| -362| 503| 362| 1E+30| $C$18| Solution x2| 0| -417| 448| 417| 1E+30| | $D$18| Solution x3| 0| -352. 0344828| 544| 352. 0344828| 1E+30| | $E$18| Solution x4| 0| -541. 0344828| 355| 541. 0344828| 1E+30| | $F$18| Solution x5| 5. 089655172| 0| 910| 1E+30| 45| | $G$18| Solution x6| 0| -165| 745| 165| 1E+30| | $H$18| Solution x7| 4. 980344828| 0| 865| 45| 106| | $I$18| Solution x8| 0| -232| 633| 232| 1E+30| | $J$18| Solution x9| 1. 83| 0| 1833| 1E+30| 223| | $K$18| Solution x10| 0| -223| 1610| 223| 1E+30| | $L$18| Solution x11| 0| -106| 759| 106| 1E+30| | $M$18| Solution x12| 0| -233| 632| 233| 1E+30| | | | | | | | Constraints| | | | | | | Â  | Â  | Final| Shadow| Constraint| Allowable| Allowable| | Cell| Name| Value| Price| R. H. Side| Increase| Decrease| | $N$10| Cheese Constraint Total| 1. 83| 968| 1. 83| 4. 980344828| 0. 379655172| | $N$11| Raw Milk Procurement Total| 11. 9| 865| 11. 9| 0. 379655172| 4. 980344828| | $N$6| Butter Constraint Total| 7. 575451034| 0| 10| 1E+30| 2. 424548966| | $N$7| Ghee Constraint Total| 0| 0| 2. 5| 1E+30| 2. 5| | $N$8| Milk Powder Constraint Total| 7. 38| 31. 03448276| 7. 38| 7. 2215| 0. 5505| | $N$9| Baby Food Constraint Total| 4. 80344828| 0| 5. 36| 1E+30| 0. 379655172| Microsoft Excel 14. 0 Sensitivity Report| | | | | | Worksheet: [DA Kamdhenu. xlsx]Sheet2 (3)| | | | | Report Created: 8/26/2011 11:47:17 AM| | | | | | | | | | | | | | | | | | | | | | Variable Cells| | | | | | | Â  | Â  | Final| Reduced| Objective| Allowable| Allowable| | Cell| Name| Value| Cost| Coefficient| Increase| Decrease| | $B$18| Solution x1| 0| -140. 5624082| 503| 140. 5624082| 1E+30| | $C$18| Solution x2| 0| -184| 448| 184| 1E+30| | $D$18| Solution x3| 0| -386. 7825206| 544| 386. 7825206| 1E+30| | $E$18| Solution x4| 0| -390. 839891| 355| 390. 7839891| 1E+30| | $F$18| Solution x5| 5. 089655172| 0| 910| 1E+30| 51. 98678414| | $G$18| Solution x6| 0| -51. 98678414| 745| 51. 98678414| 1E+30| | $H$18| Solution x7| 5. 36| 0| 865| 1E+30| 102. 2026432| | $I$18| Solution x8| 0| -102. 2026432| 633| 102. 2026432| 1E+30| | $J$18| Solution x9| 1. 83| 0| 1833| 1E+30| 118. 5653451| | $K$18| Solution x10| 0| -118. 5653451| 1610| 118. 5653451| 1E+30| | $L$18| Solution x11| 3. 172259861| 0| 759| 58. 42079208| 127| | $M$18| Solution x12| 3. 548084966| 0| 632| 127| 58. 42079208| | | | | | | | | Constraints| | | | | | Â  | Â  | Final| Shadow| Constraint| Allowable| Allowable| | Cell| Name| Value| Price| R. H. Side| Increase| Decrease| | $N$10| Cheese Constraint Total| 1. 83| 1096. 565345| 1. 83| 3. 857694581| 1. 83| | $N$11| Raw Milk Procurement Total| 19| 632| 19| 1. 268870718| 3. 548084966| | $N$6| Butter Constraint Total| 10| 186. 4904552| 10| 2. 416245862| 0. 864100959| | $N$7| Ghee Constraint Total| 1. 841456098| 0| 2. 5| 1E+30| 0. 658543902| | $N$8| Milk Powder Constraint Total| 7. 38| 113. 7839891| 7. 38| 5. 169056106| 7. 38| | $N$9| Baby Food Constraint Total| 5. 36| 103. 2026432| 5. 36| 3. 103892192| 5. 6| For Winter Months (September to April) As can be seen from the above analysis, we will supply the following products -: Winter Months – 5. 09, 4. 98 and 1. 83 units for WMP + butter, Baby Food + butter and Cheese + Butter respectively. Summer Months – WMP + Butter 5. 09, Baby food + butter 5. 38, Cheese + butter 1. 83, Standardized Milk + butter 3. 17, Standardized Milk + Ghee 3. 54 units Question3: In case you were negotiating a contract with the state, what qua ntity of FA Milk would you commit to supply? Answer: As seen by the analysis done above, the quantity of FA milk is 0. Hence, the assumption that FA Milk is the most profitable product stands invalidated. However, we have an obligation to supply to the government as the main objective of the dairy is to supply to the government. So, we will only supply the bare minimum quantity. This will never exceed the lowest value (the value for June). However, if there is no such obligation, we will not supply any milk as it is not profitable to do so. Question4: In case the dairy was planning to expand its butter churning and powder drying capacity, how much money should it invest in this expansion? Answer: The amount of money which can be spent should be less than the profit which we can make from this. Profit which can be made = shadow price * increase in capacity (till the allowable increase limit) Also, there should not be any slack i. e. excess capacity for the products. If there is already excess capacity available, we would not be expanding. Thus, the amount which can be spent for expansion of butter storage capacity = 186. 5 * 0. 864 = Rs. 161. 136 The amount which can be spent for expansion of Powder drying capacity = 113. 8 * 7. 38 = Rs. 839. 844