QUESTION 1

A local 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

government 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 R1 to make a liver-flavored biscuit and R2 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?

1.1) Formulate this as a linear programming problem.

1.2) Find the optimal solution for this problem graphically.

1.3) What is the total cost of a package of dog biscuits using the optimal mix?