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.?

Question

Business

Aimee Hogan

6 August, 14:16

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.?

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Cale Mckenzie · 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