Question

A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have the following cost structures as shown in the table. The producer knows there is a big order or order contract that will be awarded by the giant retail WalWal. The producer is not certain as what capacity production is to produce. It all depends on WalWal’s contract. The producer has also been informed, the first batch of pottery is required to ship in a very tight time frame from the first production run. The producer decides to plan ahead and select the best production process to set up for manufacturing.

Process 1	Process 2	Process 3
Ann. Fixed Cost $	8,125	13,245	6,102
variable cost $/unit	0.81	0.61	1.08

The producer wants you to help them to identify at what range of production Q (quantity) is Best to adopt Process 1, Process 2, and Process 3.

Note: To sepcify annual Q range, use 1234 < Q <= 5678.

Questions:
a) The range of annual Q for which Process 1 is best to use is:________

b) The range of annual volume for which Process 2 is best to use is: _________

c) The range of annual volume for which Process 3 is best to use is: _________

Answer 1

Here, we will find the point of indifference between Process 3 (least fixed cost) and Process 1 and after that between Process 1 & 2.

At X unit -

Total cost of Process 1 = 8125 + 0.81X

Total cost of Process 2 = 13245 + 0.61X

Total cost of Process 3 = 6102 + 1.08X

At Point of Indifference -

Total cost of Process 3 = Total cost of Process 1

6102 + 1.08X = 8125 + 0.81X

0.27X = 2023

X = 7492.59

Again,

Total cost of Process 1 = Total cost of Process 2

8125 + 0.81X = 13245 + 0.61X

0.20X = 5120

X = 25600

Basis Above, below will be the feasible quantity range.

Process 1 = 7492<Q<=25600

Process 2 = Q>=25600

Process 3 = Q<=7492