4) 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 Arequires 6 min on machine Individual problem 1-52 marks for 2% of your final grade 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 1 and 3 hr of machine time available on machine Il in each work shift How many units of each product should be produced in each shift to maximize the company's profit? (6 marks) b. A farmer plans to plant two crops. A and B. The cost of cultivating crop A is $40/acre time available on macho hine time available on machine il in each work shift How many units of each product should be produced in each shift to maximize the company's profit? (8 marks) 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? (8 marks) c. A veterinarian has been asked to prepare 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 1 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 1 and 4 units of nutrient II. Each ounce of brand B contains 5 units of nutrient 1 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. (8 marks) 4) 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 Arequires 6 min on machine Individual problem 1-52 marks for 2% of your final grade 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 1 and 3 hr of machine time available on machine Il in each work shift How many units of each product should be produced in each shift to maximize the company's profit? (6 marks) b. A farmer plans to plant two crops. A and B. The cost of cultivating crop A is $40/acre time available on macho hine time available on machine il in each work shift How many units of each product should be produced in each shift to maximize the company's profit? (8 marks) 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? (8 marks) c. A veterinarian has been asked to prepare 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 1 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 1 and 4 units of nutrient II. Each ounce of brand B contains 5 units of nutrient 1 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. (8 marks)
