Question

Arthur Meiners is the production manager of​ Wheel-Rite, a small producer of metal parts.​ Wheel-Rite supplies​ Cal-Tex, a larger assembly​ company, with 10 comma 400 wheel bearings each year. This order has been stable for some time. Setup cost for​ Wheel-Rite is ​$39​, and holding cost is ​$0.70 per wheel bearing per year.​ Wheel-Rite can produce 480 wheel bearings per day.​ Cal-Tex is a​ just-in-time manufacturer and requires that 52 bearings be shipped to it each business day. ​a) What is the optimum production​ quantity? nothing units ​(round your response to the nearest whole​ number).

Answer 1

The optimum production quantity is 72 wheel bearings per batch.

Step-by-step explanation:

Wheel Rite can produce 480 wheel bearings per day.

Setup cost are $39 per batch.

Holding costs are $0.70 per unit per year.

The optimum batch size can be calculated as the one that minimizes the cost. This can be calculated with the Economic Order Quantity formula:

`Q=\sqrt{(2DS)/(H) }`

In this case, the units are:

D: daily demand (52 u.)

S: Setup cost per order ($39)

H: holding cost per unit per year ($0.70)

Then, we have:

`Q=\sqrt{(2DS)/(H) }=\sqrt{(2*52*39)/(0.7) }=√(5,794)=76.12\approx 72`

The optimum production quantity is 72 per batch.