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

Answer:

The optimum production quantity is 72 wheel bearings per batch.

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:

$Q=\sqrt{\frac{2DS}{H} }$

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:

$Q=\sqrt{\frac{2DS}{H} }=\sqrt{\frac{2*52*39}{0.7} }=\sqrt{5,794}=76.12\approx 72$

The optimum production quantity is 72 per batch.