A producer of pottery is considering the addition of a new plant to absorb the b

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 $

6,125

9,878

3,871

variable cost $/unit

0.68

0.54

1.18

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:

P.S. I ALSO DO NOT KNOW HOW THE ANSWER SHOULD BE WRITTEN FOR a), b), and c)

Process 1

Process 2

Process 3

Ann. Fixed Cost $

6,125

9,878

3,871

variable cost $/unit

0.68

0.54

1.18

Explanation / Answer

Step 1: Find the indiffernce between all the three process. you will get three indifference point.

Step 2: Find the total Cost at that indiffrence point for all the three process.

Step 3: Compare the Total cost of all the three process.

Step 4: Process with minimum total cost will be best to use at that Annual quantity level.

Total Cost = Fixed Cost + (Variable Cost * Quantity)

Annual Q range, use 1234 < Q <= 5678 (Given in question)

Point of indifference between process 1 and process 2

FC + VC * Q = FC + VC * Q

6125 + 0.68Q = 9878 + 0.54Q

Q = 26,807

Point of indifference between process 2 and process 3

FC + VC * Q = FC + VC * Q

9878 + 0.54Q = 3871 +1.18Q

Q = 9386

Point of indifference between process 1 and process 3

FC + VC * Q = FC + VC * Q

6125 + 0.68Q = 3871 +1.18Q

Q = 4508

(A) The range of annual Q for which Process1 is best to use is 4508 <= Q <= 5678.

(B) The range of annual volume for which Process 2 is best to use is Q <= 26807.

(C)  The range of annual volume for which Process 3 is best to use is 1234 < Q <= 4508

I have calculated the cost in the given table. For your understanding i have calculated at different Q level so that you can compare the total cost to decide the process.

* Note : Bold indicate the indifference point comparison. In question (a) Q limit is 1234 < Q <= 5678 therefore answer is given above. But , If the Q limit is not given answer will be 4508 <= Q <= 26087.

You can compare the Total cost with respect to the Quantity (Q) in the table to undersatnd.

Process 1 Process 2 Process 3 Q FC VC/Unit TVC(VC*Q) Total Cost Q FC VC/Unit TVC(VC*Q) Total Cost Q FC VC/Unit TVC(VC*Q) Total Cost 1235 6125 0.68 839.8 6965 1235 9878 0.54 666.9 10545 1235 3871 1.18 1457 5328 1350 6125 0.68 918 7043 1350 9878 0.54 729 10607 1350 3871 1.18 1593 5464 1400 6125 0.68 952 7077 1400 9878 0.54 756 10634 1400 3871 1.18 1652 5523 1500 6125 0.68 1020 7145 1500 9878 0.54 810 10688 1500 3871 1.18 1770 5641 1600 6125 0.68 1088 7213 1600 9878 0.54 864 10742 1600 3871 1.18 1888 5759 2000 6125 0.68 1360 7485 2000 9878 0.54 1080 10958 2000 3871 1.18 2360 6231 3000 6125 0.68 2040 8165 3000 9878 0.54 1620 11498 3000 3871 1.18 3540 7411 4000 6125 0.68 2720 8845 4000 9878 0.54 2160 12038 4000 3871 1.18 4720 8591 4500 6125 0.68 3060 9185 4500 9878 0.54 2430 12308 4500 3871 1.18 5310 9181 4508 6125 0.68 3065.44 9190 4508 9878 0.54 2434 12312 4508 3871 1.18 5319 9190 5000 6125 0.68 3400 9525 5000 9878 0.54 2700 12578 5000 3871 1.18 5900 9771 5500 6125 0.68 3740 9865 5500 9878 0.54 2970 12848 5500 3871 1.18 6490 10361 5678 6125 0.68 3861.04 9986 5678 9878 0.54 3066 12944 5678 3871 1.18 6700 10571 7000 6125 0.68 4760 10885 7000 9878 0.54 3780 13658 7000 3871 1.18 8260 12131 9000 6125 0.68 6120 12245 9000 9878 0.54 4860 14738 9000 3871 1.18 10620 14491 9386 6125 0.68 6382.48 12507 9386 9878 0.54 5068 14946 9386 3871 1.18 11075 14946 10,000 6125 0.68 6800 12925 10,000 9878 0.54 5400 15278 10,000 3871 1.18 11800 15671 20,000 6125 0.68 13600 19725 20,000 9878 0.54 10800 20678 20,000 3871 1.18 23600 27471 26,807 6125 0.68 18228.8 24354 26,807 9878 0.54 14476 24354 26,807 3871 1.18 31632 35503 30,000 6125 0.68 20400 26525 30,000 9878 0.54 16200 26078 30,000 3871 1.18 35400 39271

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