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 $	7,017	9,035	14,251
variable cost $/unit	1.05	0.78	0.63

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

Let the required quantity = N

Total cost = Fixed cost + Variable cost / unit x N

The range for which process 1 is best :

Total cost of process 1 < total cost of process 2

Or, 7017 + 1.05.N < 9035 + 0.78.N

Or, 1.05.N – 0.78.N < 9035 – 7017

Or, 0.27.N < 2018

Or, N < 2018/0.27 = 7474.07

Total cost for process 1 < Total cost for process 3

Or, 7017 + 1.05.N < 14251 + 0.63.N

Or, 0.42.N < 7234

Or, N < 17223.80

Taking into account both, it should be N < 7474.07 ( I.E. from 0 to 7474)

The range for which process 2 is best :

Total cost for process 2 < Total cost for process 1

9035 + 0.78.N < 7017 + 1.05N

Or, 1.05.N – 0.78.N > 9035 – 7017

Or, 0.27.N > 2018

Or, N > 7474.07

Total cost for process 2 < Total cost for process 3

9035 + 0.78.N < 14251 + 0.63.N

Or, 0.15.N < 5216

Or, N < 34773.33

Taking into account both , N will be in the range of 7475 and 34773

The range for which process 3 is best :

Total cost for process 3 < Total cost for process 1

Or, 14251.63 + 0.63.N < 7017 + 1.05.N

Or, 0.42.N > 7234.63

Or, N > 17225.30

Total cost for process 3 < Total cost for process 2

14251.63 + 0.63.N < 9035 + 0.78.N

Or, 0.15N > 5216.63

Or, N > 34777.53

Taking into account of both, N > 34773.33

ANSWER :

The range of annual Q for which process 1 is best to use : 0 to 7474

The range of annual Q for which process 2 is best to use :7475 to 34773

The range of annual Q for which process 3 is best to use :34774 and above