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 14 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.?

Answer 1

Given

Variables:

X= liver flavored biscuits

Y= number of chicken flavored

Objective function: Minimum Z

Min Z = 1X + 2Y

Subject to

1X+1Y >= 40

2X+4Y >= 60

1X + 0Y <=16 (or) 1X <=16

X,Y>=0

Optimal solution X = 16 , Y = 24 and Z = 64