The Fido Dog Food Company wishes to introduce new brand of dog biscuits (composed of chicken as wll as liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits have 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones have 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there should be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make chicken-flavored one, determine the optimal product mix for a package of the biscuits in order to minimize the firm's cost?
a) Formulate this as a linear programming problem.
b) Compute the optimal solution for this problem graphically.
c) Are any constraints redundant? If so, which one or ones?
d) What is the total cost of a package of dog biscuits using the optimal mix?