A farm occupies 200 acres of land and has £10000 available for investment. The family whorun the farm can work for a total of 5000 work-hours during the winter and 7000 work-hoursfor the rest of the year. If any of these work-hours are not needed then the family will usethem to help at the local village store, earning a profit of £9 per hour (regardless of the timeof year). Past experience shows the family will not have more than 50 spare work-hours towork in the village store during the winter and not more than 80 over the summer.The farm brings in cash for the family from three crops (lettuces, carrots, and swedes) andtwo types of livestock (dairy cows and hens). The family would like to maximise their cashincome. The crops need no investment funds but each cow requires an initial investment of£1000 and each hen £10. Each cow needs 1.5 acres of land and the size of the barn limits thenumber of cows in the herd to 20. Each cow also require 100 work hours during the winterand 60 hours during the rest of the year. The hens do not need any specific land, but the farmcan accommodate a maximum of 100 hens. To look after them well, each hen needs 1.1work hours during the winter and 0.8 work hours during the rest of the year. A cow bringsin a net annual income of £400 while a hen generates £3.Crops also generate income and require work hours to tend to them. The table below sum-marises such information:crop winter work hours summer work hoursLettuceCarrotsSwede202510104010income (per acre)£100£130£110Formulate this scenario as a linear programming problem, making sure you clearly and fullydefine your decision variables, constraints, and objective function.

Let x be the number of cows, y be the number of hens, l be the number of acres for lettuce, c be the…

Answered: Formulate this scenario as a linear…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 54P

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It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
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A plant operation has a fixed costs of $2,000,000 per year and its output capacity is 100,000 electrical appliances per year. The variable cost is $40 per unit and the product sells for $90 per unit. Compare annual profit when the plant is operating at 90% of capacity with the plant operation at 100% capacity. Assume that the first 90% of capacity output is sold at $90 per unit and that the remaining 10% of production is sold at $70 per unit.
Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer). She estimates thatshe will receive an annual return of $8,000 for each condominium and $6,000 for each acre of land. A condominium unit costs $70,000, and land costs $30,000 per acre. A condominium will cost her $1,000 per unit. an acre of land will cost $2,000 for maintenance and upkeep, and $14,000 has been budgeted for these annual expenses. Lauren wants to know how much to invest in condominiums and land to maximize her annual return. a. Formulate a mixed integer programming model for this problem. b. Solve this model by using the computer.
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Formulate this scenario as a linear programming problem, making sure you clearly and fully define your decision variables, constraints, and objective function.