2 There are three alternatives available to meet the demand

2. There are three alternatives available to meet the demand of a particular product. They are as follows: (a) Manufacturing the product by using process A (b) Manufacturing the product by using process B (c) Buying the product. The details are as given in the following table: Cost Elements Manufacturing the Manufacturing the Buy product by usingprduct by using Fixed costyear Variable cost/unit Purchase cost/ unit process A $400,000 process B 200,000 50 35 110 a- b- c- Determine the breakeven points for each pair of the options. Specify the range at which each option should be selected. If the annual demand of the product is 8,000 units. Should the company make the product using process A or process B or buy it?

Solution

a)

Consider the given problem here there are two process “A” and “B” to produce the good. So, under process “A” and “B” the cost functions are given by.

=> “Ca(q) = 400,000 + 35*q”, and “Cb(q) = 200,000 + 50*q”, respectively. Now, the price of the good is “110”.

So, under the process “A” the break even condition is given by.

=> 400,000 + 35*q = 110*q, => 75*q = 400,000, => q = 400,000/75 = 5,333.33, => q = 5,333.33.

Now, under the process “B” the break even condition is given by.

=> 200,000 + 50*q = 110*q, => 60*q = 200,000, => q = 200,000/60 = 3,333.33, => q = 3,333.33.

So, here under “process A” and “process B” the break even points are “P=110, q=5,333.33” and “P=110, q=3,333.33” respectively.

b).

So, let’s assume that “qc” be the level of output where “Ca” is equal to “Cb”.

=> 400,000 + 35q = 200,000 + 50*q, => 15*q = 200,000, => q = 200,000/15 = 13,333.33 = qc.

So, if “q < qc = 13,333.33”, => “Cb < Ca”, => process “B” should be selected. Now, if “q > qc = 13,333.33”, => “Cb > Ca”, => process “A” should be selected.

c).

Now, if “q=8,000”, => the cost under process “A” is given by, “Ca = 400,000 + 35*8,000 = 680,000. Similarly, if “q=8,000”, => the cost under process “B” is given by, “Cb = 200,000 + 50*8,000 = 600,000. Now, if the company purchases it then the total cost is given by, => 110*8,000 = 880,000. So, if we compare these costs, => the lowest cost is “600,000” corresponds the process “B”. So, here the company will produce it through process “B”.