Question

A company is about to begin production of a new product. The manager of the department that will produce one of the components for the new product wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of 200 units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, 50 weeks a year. The manager estimates that it will take a full day to get the machine ready for a production run, at a cost of $250. Inventory holding costs will be $10 a year.
Required:
a. What run quantity should be used to minimize total annual costs?
b. What is the length of a production run in days?
c. During production, at what rate will inventory build-up?
d. lf the manager wants to run another job between runs of this item, and needs a minimum of 10 days per cycle for the other work, will there be enough time?
e. Given your answer to part d, the manager wants to explore options that will allow this other job to be performed using this equipment. Name three options the manager can consider.
f. Suppose the manager decides to increase the run size of the new product. How many additional units would be needed to just accommodate the other job? How much will that increase the total annual cost?

Answer 1

Answer:

Kindly check explanation

Explanation:

Given that :

Production rate (p) = 200 units / day

daily usage (d) = 80 units / day

Assembly, a = 5 days a week ; 50 weeks a year

Setup cost (S) = $250

Holding cost (H )= $10

A) Run quantity to minimize total annual cost:

√(2DS/H) * √p / (p - d)

D = annual demand = (80 * 5 * 50) = 20,000

√(2(20000)(250)/10) * √200 / (200 - 80)

1000 * 1.2909944

= 1290.99

= 1291 units

B) Run length :

1291 / 200 = 6.455 days

C) Inventory build up:

Daily production - daily usage:

(200 - 80) = 120 units / day