Question

he Wood Valley Dairy makes cheese to supply to stores in its area. The dairy can make 485 pounds of cheese per day (358 days per year), and the demand at area stores is 67 pounds per day. Each time the dairy makes cheese, it costs $290 to set up the production process. The annual cost of carrying a pound of cheese in a refrigerated storage area is $0.92. Determine the minimum total annual cost.

Answer 1

Minimum total annual cost = $3,321.26

Explanation :

The computation of the minimum total annual cost is shown below:

As per the data given in the question,

Annual demand (D) = 67 × 358 days = 23,986

Setup cost (C) = $290

Production rate (R) = 358 days × 485 = 173,630

Holding cost(H) = $0.92

Economic production quantity(Q) = sqrt((2 × D × C) ÷ H × (1-(D ÷ R)))

= sqrt(((2 × 23,986 × $290) ÷ $0.92 × (1 -(23,986 ÷ 173,630)))

= 4,188.7

= 4,189

Minimum total annual cost is

= (Q ÷ 2) × (1 - D ÷ R) × H + (D ÷ Q) × C

=4,189 ÷ 2 × (1 - (23,986 ÷ 173,630) × $0.92+ (23,986 ÷ 4,189) × 290

= $3,321.26