The Pretty Cat Company wishes to introduce a new brand of cat dry foods that meets certain nutritional requirements. The biscuit-1 contains 2 units of nutrient A and 4 units of nutrient B, while biscuit-2 contains 2 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 80 units of nutrient A and 120 units of nutrient B in a package of the new dry food (biscuit mix). In addition, the company has decided that there can be no more than 30 biscuit-1 in a package. If it costs 2 cents to make a biscuit-1 and 4 cents to make a biscuit-2, what is the optimal product mix for a package of the new dry food in order to minimize the firm's cost? (a) Formulate this as a linear programming problem. (b) Find the optimal solution for this problem graphically. What is the total cost of a package of the new dry food using the optimal mix?
The Pretty Cat Company wishes to introduce a new brand of cat dry foods that meets certain nutritional requirements. The biscuit-1 contains 2 units of nutrient A and 4 units of nutrient B, while biscuit-2 contains 2 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 80 units of nutrient A and 120 units of nutrient B in a package of the new dry food (biscuit mix). In addition, the company has decided that there can be no more than 30 biscuit-1 in a package. If it costs 2 cents to make a biscuit-1 and 4 cents to make a biscuit-2, what is the optimal product mix for a package of the new dry food in order to minimize the firm's cost?
(a) Formulate this as a linear programming problem.
(b) Find the optimal solution for this problem graphically. What is the total cost of a package of the new dry food using the optimal mix?
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