The Poppy Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavored biscuits) that meets certain nutritional requirements. The liver-flavored biscuits contain 2 units of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 2 units of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 30 units of nutrient A and 40 units of nutrient B in a package of the new biscuit mix. In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a chicken-flavored one, what is 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) Find the optimal solution for this problem graphically. (c) Are there more than one solution? What is the advantage of having many solutions in decision-making? (d) What is the total cost of a package of dog biscuits using the optimal mix?