Question

Doug Turner Food Processors 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. It costs 1​¢ to make 1 liver flavored biscuit and 2​¢ to make 1 chicken flavored. Doug wants to determine the optimal product mix for a package of the biscuits to minimize the​ firm's cost.

The aim of the objective function should be to ▼ Minimize Maximize the objective value.

The optimum solution​ is:

Number of liver flavored biscuits in a package​ = ___ ​(round your response to two decimal​ places).

Number of chicken flavored biscuits in a package​ = ____ ​(round your response to two decimal​ places).

Optimal solution value​ = ____ ​(round your response to two decimal​ places).

Answer 1

We tabulate the given data as shown below:

Let the number of Liver Flavored Biscuits be x and No. of Chicken Flavoured biscuits be y

Hence, the Total Cost of biscuits = 0.01 * x + 0.02 * y

We have to minimize the costs

The aim of the objective function should be to Minimize the objective value.

Hence, the Objective function

Minimize Total Costs = C = 0.01 * x + 0.02 * y

Subject to constraints:

1*x + 1*y >= 40............Minimum requirement of Nutrient A

2x + 4y >= 60...............Minimum Requirement of Nutrient B

x <= 15........................Max. no. of Liver flavored biscuits in a package

x, y >= 0 ......................Non-negativity Constraints

Solving the above in Excel Solver we get,

The above solution in the form of formulas along with Solver Extract is shown below for better understanding and reference:

As seen from solution,

The optimum solution​ is:

Number of liver-flavored biscuits in a package​ = 15.00

Number of chicken flavored biscuits in a package​ = 25.00

Optimal solution value​ = $0.65

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