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 $	2,891	4,898	10,014
variable cost $/unit	0.91	0.65	0.51

  
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

	Process 1	Process 2	Process 3
Ann. Fixed Cost $	2,891	4,898	10,014
variable cost $/unit	0.91	0.65	0.51

We need to compare the total cost of these three processes to find the quantity range for which each process is best

Total cost = Fixed cost + Variable cost * No. of units produced

Total cost for 1 unit produced

Process 1 = 2891+0.91*1 = 2891.91

Process 2 = 4898+0.65*1 = 4898.65

Process 3 = 10014+0.51*1 = 10014.51

For 1 unit Process 1 is best as it has the lowest total cost.

The cost will be lowest to a point where any of the other two processes would have an equal total cost. From that point Process 1 would have a higher total cost than the other process.

To find the point process 2 and 3 should be compared with process 1 to find the point at which each one would have equal total cost with process 1

Comparing Process 1 and 2

Let the unit be x at which these two processes would have the equal total cost.

The total cost of P1 = 2891+0.91x

The total cost of P2 = 4898+0.65x

2891+0.91x = 4898+0.65x

=> 0.91x - 0.65x = 4898 - 2891

=> x = (4898 - 2891)/(0.91 - 0.65) = 7719.23

At 7720 units process 2 has a lower cost than process 1

Now comparing Process 1 and Process 3:

The unit at which these two would have equal cost = (10,014-2,891)/(0.91-0.51) = 17807.5

At 17808 process 3 would have a lower total cost than process 1

Now, calculating the total cost of process 2 and 3 at 17808

Process 2 = 4898+0.65*17808 = 16473.2

Process 3 = 10014+0.51*17808 = 19096.08

Though Process 3 has lower cost than Process 1, process 2 is lowest at 17808 units. Hence process 3 is not best at this point and process 2 continues to be the best after 7719.23 and till 17808. (the upper limit is yet to be found)

Hence, Process 1 is best for the unit range of 1 to 7719.23

The lower limit of quantity range for Process 2 is known which is 7719.23 but to find the upper limit, we need to find the quantity at which process 2 stops being best and process 3 becomes best

The quantity at which process 2 and 3 have equal total cost = (10014-4898)/(0.65-0.51) = 36542.86

At 36543 units Process 2 would have a higher total cost than the process 3.

Hence Process 2 is best for a quantity range of 7719.23 to 36542.86

Process 3 has lowest cost for a range of 36542.86 and more.

a) The range of annual Q for which Process 1 is best to use is: 0 < Q <= 7719.23

b) The range of annual volume for which Process 2 is best to use is: 7719.23 < Q <= 36542.86

c) The range of annual volume for which Process 3 is best to use is: 36542.86 < Q and more