Please explain in detail how to solve part a b c and d pleas

Please explain in detail how to solve part (a), (b), (c), and (d) please.

16) The Fido 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 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient Bin 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 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?

Solution

Let X = number of liver-flavored biscuits Y=number of chicken-flavored biscuits Objective: Minimize cost------C=$0.01X+0.02Y Constraints: X+Y>=40 2X + 4Y >= 60 X<=15 X,Y>=0