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 $	5,291	14,582	8,835
variable cost $/unit	1.25	0.63	0.83

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

Enter Q range with whole number and use signs such as <= and >= to describe greater or less than equal to. Ex. 1234 < Q <= 5678

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

Solution:

The quantity would be best to use if it produces a lower total cost. Hence,

We first compare the process 1 and 3. Hence, let x be the number of units.

Also,

We now compare 2nd and third process to get,

Hence,

a: The range of annual Q for which Process 1 is best to use is x <= 8438

b: The range of annual Q for which Process 2 is best to use is x > 28735

c: The range of annual Q for which Process 3 is best to use is 8438 < x <= 28735