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 $ 8,125 13,245 6,102 variable cost $/unit 0.81 0.61 1.08 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:

Explanation / Answer

Process 1: fixed cost = 8,125 and variable cost = 0.81 per unit

Process 2: fixed cost = 13,245 and variable cost = 0.61 per unit

Process 3: fixed cost = 6,102 and variable cost = 1.08 per unit

let the quantity be 0 - 1,000 units.

I do an excel simulation starting from Q = 0 to determine the situation where each process offers the lowest cost. Total cost for a process = fixed costs+Q*variable costs

We find that at Q = 7493 units, process 1 has the lowest cost as shown in the table below:

This extends upto 25,559 units when the cost of process 1 is the lowest.

Thus the annual Q for process 1 : 7,492<Q<=25,559 units

b. Process 2's cost is lowest in the range 25,600 units and more. At 25,600 units the cost of process 1 and process 2 is the same. From 25,601 units and any amount greater than this process 2 will be preferred.

So for process 2: Q>=25,600 units.

c. Process 3 has the lowest cost in the 0 to 7,492 units.

Thus for process 3: 0<Q<=7492

Q 7493 Process 1 Fixed cost 8,125.00 8,125.00 Variable cost 0.81 6,069.33 Total cost 14,194.33 Process 2 Fixed cost 13,245.00 13,245.00 Variable cost 0.61 4,570.73 Total cost 17,815.73 Process 3 Fixed cost 6,102.00 6,102.00 Variable cost 1.08 8,092.44 Total cost 14,194.44

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