Question

Ed Silver Dog Food Company wishes to introduce a new brand of dog biscuits composed of chicken-and liver-flavored biscuits that meet certain nutritional requirements. The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B; the chicken- flavored biscuits 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-flavored biscuits in a package. If it costs 1 cent to make 1 liver- flavored biscuit and 2 cents to make 1 chicken-flavored, what is the optimal product mix for a package of the biscuits to minimize the firm's cost? Formulate this as a linear programming problem

Answer 1

The question involves formulating a linear programming problem to find the optimal mix of liver- and chicken-flavored biscuits to minimize costs while meeting nutritional and quantity constraints.

Step-by-step explanation:

The question presented requires the formulation of a linear programming problem to determine the optimal product mix for a new brand of dog biscuits given certain constraints and cost parameters. The variables we need to define are the number of liver-flavored biscuits (let's call this 'x') and the number of chicken-flavored biscuits (let's call this 'y'). The objective function, which we want to minimize, is the cost of producing these biscuits: Cost = 1x + 2y cents. The constraints based on the nutritional requirements and company decision are as follows:

• Nutrient A: x + y ≥ 40
• Nutrient B: 2x + 4y ≥ 60
• Liver-flavored biscuit limitation: x ≤ 15
• Non-negativity: x, y ≥ 0

The company wants to determine the values of 'x' and 'y' that will satisfy these constraints while minimizing the total cost.