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 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 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?
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