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The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavoured biscuits) that meets certain nutritional requirements. The liver-flavoured biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavoured 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 mix. In addition, the company has decided that there can be no more than 15 liver-flavoured biscuits in a package. If it costs 1 cent to make a liver-flavoured biscuit and 2 cents to make a chicken-flavoured 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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