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 11 comma 300 wheel bearings each year. This order has been stable for some time. Setup cost for​ Wheel-Rite is ​$39​, and holding cost is ​$0.50 per wheel bearing per year.​ Wheel-Rite can produce 530 wheel bearings per day.​ Cal-Tex is a​ just-in-time manufacturer and requires that 49 bearings each business day.

a) What is the optimum production quantity?
b) What is the maximum number of wheel bearings that will be in inventory at Wheel-Rite?
c)How many production runs of wheel bearings will Wheel-Rite have in a year?
d)What is the toal setup plus holding cost for Wheel-Rite?

Answer 1

Answer:

a. 1,217

b. 1095

c. 8.22

d. $657.30

Explanation:

a)

The optimum production quantity is the Economic Production Quantity, EPQ, given that the production rate p = 500 wheel bearings per day

The demand D = 10,000 wheel bearings per year

The holding costs H = $0.06 per wheel bearing per year the ordering cost S = $40 per order using the formula

$EPQ =\sqrt{ \frac{2D \times S}{H \times [1 - \frac{d}{p}]}}$

where the demand  or consumption rate  per day d = 50

substitute in equation (1) the values of D = 10,000, S = $40, H = $0.60, d = 50 and p = 500 to obtain

$EPQ =\sqrt{ \frac{2\times 10,000 \times 40}{0.60 \times [1 - \frac{50}{500}]}}$

= 1,217.2

the optimum production Quantity = 1,217 wheel bearings

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