Reference no: EM132834579

Develop a mathematical model to be solved for each of the following examples:(Write down the function to be maximized/minimized and write down all the constraints/limitations associated with each case)

a. A company manufactures two products, A and B, on two machines, I and II. It has been determined that the company will realize a profit of $3/unit of product "A" and a profit of $4/unit of product "B". To manufacture a unit of product "A" requires 6 min on machine I and 5 min on machine II. To manufacture a unit of product "B" requires 9 min on machine I and 4 min on machine II. There are 5 hr of machine time available on machine I and 3 hr of machine time available on machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?

b. A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre whereas that of crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit?

c. A veterinarian has been asked to make a diet for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 8 oz and must contain at least 29 units of nutrient I and 20 units of nutrient II. The vet has decided that the diet may be prepared from two brands of dog food: brand A and brand B. Each ounce of brand A contains 3 units of nutrient I and 4 units of nutrient II. Each ounce of brand B contains 5 units of nutrient I and 2 units of nutrient II. Brand A costs 3 cents/ounce and brand B costs 4 cents/ounce. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost.