Question

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 4 units of nutrient B, while the chicken-flavored ones contain 2 unit of nutrient A and 2 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 chicken-flavored biscuits in a package. It costs 2 cent to make a liver-flavored biscuit and 1 cents to make a chicken-flavored one.

Let       X1 = number of liver-flavored biscuits in a package

            X2 = number of chicken-flavored biscuits in a package

Formulate this as a linear programming problem and answer the following

What is an appropriate objective function? (Choose from below)

Minimize 1X1 + 2X2

Maximize 2X1 + 1X2

Maximize 1X1 + 2X2

Minimize 2X1 + 1X2

What is an appropriate constraints?

• 4X1 + 2X2 ≥ 40 AnswerYesNo
• X2 ≥ 15 AnswerYesNo
• X2 ≤ 15 AnswerYesNo
• 4X1 + 2X2 ≥ 60 AnswerYesNo
• X1 + 2X2 ≥ 40 AnswerYesNo
• X1 + 2X2 ≤ 40 AnswerYesNo
• X1, X2 ≥ 0 AnswerYesNo
• X1, X2 ≤ 0 AnswerYesNo

Answer 1

Formulate the problem as shown below:

Let, x1 be the quantity of liver flavoured biscuits

       x2 be the quantity of chicken flavoured biscuits.

The question consists the information about the cost of both Chicken flavoured and liver flavoured biscuits. So, we have to minimize the cost of production of biscuits for the company.

Based on the above statement, the Objective function will be:

Minimize Z   2x1 + x2

The Constraints are mentioned below:

The quantity of nutrient A for liver flavoured biscuit is 1 unit and for chicken flavoured is 2 units. Also, there must be at least 40 units of nutrient A.

x1 + 2x2 ≥ 40 ……(1)

The quantity of nutrient B for liver flavoured biscuit is 4 units and for chicken flavoured is 2 units. Also, there must be at least 60 units of nutrient B.

4x1 + 2x2 ≥ 60 …….(2 )

Also, the company has decided to not put more than 15 chicken flavoured biscuits in a packet.

x2 ≤ 15 …….(3)

and last, the quantities of both flavoured biscuits must be greater than zero.

x1, x2 ≥ 0. …….(4)