Answer:
46,734 units per run
Explanation:
total estimated demand = 700,000 containers
setup costs per production run = $546
manufacturing cost = $0.47 per container
holding cost = $0.35 per container
r = 700,000 / x
total setup costs = 546r = 546 (700,000/x) = 382,200,000/x
production costs = 0.47 x 700,000 = 329,000
storage cost per unit= 1/2r x 0.35 = 0.35/2(700,000/x) = 0.35x/1,400,000
total storage costs = 700,000 x 0.35x/1,400,000 = 0.175x
C(x) = 382,200,000/x + 0.175 x + 329,000
now we find the derivative:
C'(x) = -382,200,000/x² + 0.175
382,200,000/x² = 0.175
382,200,000 = 0.175x²
x² = 382,200,000 / 0.175 = 2,184,000,000
x = √2,184,000,000 = 46,733.28 ≈ 46,734 units per run
this answer is based on a continuous production process, there are 14.98 runs per year
