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 2Process 3 Process 1 8,125 13,245 0.61 6,102 1.08 Ann. Fixed Cost S variable cost S/unit0.81 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

Explanation / Answer

We are given three processes having different annual fixed costs and different variable costs.

The Production cost equation will be as below:

Production Cost (PC)= FC + (VC X Q)

where, FC = Annual Fixed Cost
VC = Variable Cost
and Q=Production Quantity

Now Process 3 is the process with the lowest fixed cost and thus will be cheapest at production

PC3 = FC3 + (VC3 X Q) - let us mark this as eqn. 1

As per eqn 1 as Q increase PC3will keep on increasing. Now, Process 1 has the next lowest fixed cost and a lower variable cost than Process 3 and therefore after a certain increase in the quantity Process 1 will start giving a lower production cost. This transition will take place at a level where production costs from both Process 1 and 3 equalise.

So if PC1= FC1 + (VC1 X Q) --- eqn 2

then, PC1=PC3
which means, FC1 + (VC1X Q) = FC3 + (VC3 X Q)

putting values, 8125+0.81 Q = 6102 + 1.08Q

8125-6102 = 1.08Q-0.81Q

2023 = 0.27Q

Q=7492.6 = approx. 7493

So, for Q<7493, Process 3 is cheapest and therefore best to use.

Similarily, As per eqn 2 as Q increase PC1will keep on increasing. Now, Process 2 has the next lowest fixed cost and a lower variable cost than Process 1 and therefore after a certain increase in the quantity, Process 2 will start giving a lower production cost. This transition will take place at a level where production costs from both Process 1 and 2 equalise.

So if PC2= FC2 + (VC2X Q)

then, PC1=PC2
which means, FC1 + (VC1X Q) = FC2 + (VC2 X Q)

putting values, 8125+0.81 Q = 13245+ 0.61Q

13245-8125 = 0.81Q-0.61Q

5120 = 0.2 Q

Q = 5120/0.2 = 25600

So, Process 3 has lowest cost for Q<7493,

Process 1 has lowest cost for Q between 7492 and 25600 i.e. 7492<Q<25600

and Process 2 has lowest cost for Q >25600

END OF SOLUTION

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