Answer :
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
