QUESTION 4 18 points Save A producer of pottery is considering the addition of a

Question

QUESTION 4 18 points Save 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 Costs l | 4,898 ¡0,014 0.51 2,891 variable cost S/unit 0.91 0.65 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 ee and >-to describe greater or less than equal to. Ex. 1234

Explanation / Answer

Total cost = Annual fixed cost + (Variable cost per unit )x Number of units

Let the number of units = N

Therefore ,

Total cost through Process 1 = 2891 + 0.91.N

Total cost through Process 2 = 4898 + 0.65.N

Total cost through Process 3 = 10014 + 0.51.N

When process 1 is best, its total cost should be less than total cost of Process 2 as well as Process 3.

Therefore ,

2891 + 0.91 N < 4898 + 0.65.N

Or, 0.26.N < 2007

Or, N < 7719.23

2891 + 0.91.N < 10014 + 0.51.N

Or, 0.4.N < 7123

Or, N < 17087.5

Taking into account both the above constraints simultaneously, we get N < 7719.23

When Process 2 is best, its total cost should be less than total cost of Process 1   as well as Process 3

Therefore ,

4898 + 0.65N < 2891 + 0.91N

Or, 0.26.N > 2007

Or, N > 7719.23

4898 + 0.65.N < 10014 + 0.51.N

Or, 0.14N < 5116

Or, N < 36542.85

Taking into account both constraints simultaneously ,

7719.23 < N < 36542.85

When Process 3 is best , its total cost should be less than total cost of Process 1 as well as Process 2

10014 + 0.51.N < 2891 + 0.91.N

Or, 0.4N > 7123

Or, N > 17807.5

10014 + 0.51.N < 4898 + 0.65.N

Or, 0.14.N > 5116

Or, N > 36542.85

Taking into account both constraints simultaneously, N > 36542.85

So,

1)The range of annual q for which process 1 is best to use : 1 to 7719
2)The range of annual q for which process 2 is best to use : 7720 to 36542
3)The range of annual q for which process 3 is best to use : 36543 and above

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