GizmoWorld sells 6000 gizmos per year. Acme charge a flat fee of exist400 per or

Question

GizmoWorld sells 6000 gizmos per year. Acme charge a flat fee of exist400 per order, plus exist25 for shipping each gizmo. Due to insurance costs, it costs GizmoWorld exist300 to store a gizmo for a year. Let x be the number of gizmo order at one time. (a) What is GizmoWorld's carrying cost? (b) What is GizmoWorld's reordering cost? (c) What is GizmoWorld's total cost? (d) How many times per year and how many gizmos should GizmoWorld order at one time to minimize their inventory costs for the year?

Explanation / Answer

a) carrying cost = 300 * (x/2)

b) reordering cost = (400 + 25 * x) *6000/x

c)total cost = 150x + 400*6000/x + 6000*25

d)Z = 150x + 400*6000/x + 6000*25

to minimize Z

dZ/dx = 0

150 - 400*6000/x^2 =0

x =40*sqrt(10) = 126.49

around 127 be the number of items order at one time

number of orders = 6000/127 =47.34 = 48 orders

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