cost functions

Virtual Assistant Help

The cost functions for the three locations are as given below:

Location A

Total Cost = 100,000 + 20Q

Location B

Total Cost = 150,000 + 15Q

Location C

Total Cost = 125,000 + 18Q

We first determine the production quantity at which Location A and Location B will have same cost.

Solving we have

100,000 + 20Q = 150,000 + 15Q

Or, Q = 10,000

 

Next we determine the production quantity at which Location A and Location C will have same cost.

Solving we have

100,000 + 20Q = 125,000 + 18Q

Or, Q = 12,500

 

Next we determine the production quantity at which Location B and Location C will have same cost.

Solving we have

150,000 + 15Q = 125,000 + 18Q

Or, Q = 8,333.33 or approximately 8,333.34

 

 

 

 

We determine the cost at each location for different production levels using the cost functions as shown below:

 

With respect to the break-even points, till production quantity of 8,333.33 Location C has a lower cost than Location B while above production quantity of 8,333.33 Location B has a lower cost than Location C.

Similarly till production quantity of 10,000 Location A has a lower cost than Location B while above production quantity of 10,000 Location B has a lower cost than Location A. Again till production quantity of 12,500 Location A has a lower cost than Location C while above production quantity of 12,500 Location C has a lower cost than Location A.

Combining all three we can see that till the production quantity of 10,000 Location A has the lowest cost among the three alternatives. For production exceeding 10,000 Location B has the lowest cost among all the three alternatives.

Hence for production quantity 0-10,000 Location A is the best alternative while for production quantity above 10,000 Location B is the best alternative.