Question

The owners of Whitewater rafting are currently contemplating a manufacturing process (Old Process) that will require an investment of $4,000 and a variable cost of $6 per raft vs. a larger (New Process) initial investment of $20,000 with more automated equipment that would reduce their variable cost of manufacture to $2 per raft. Compare the two manufacturing processes proposed here. For what volume demand should each process be chosen?

A. From 0 to 1000 choose Old Process, From 1000 to infinity choose New Process
B. From 0 to 4000 choose New Process, From 4000 to infinity choose Old Process
C. From 0 to 4000 choose Old Process, From 4000 to infinity choose New Process
D. Always use the Old Process and never use the New Process
E Always use the New Process and never use the Old Process

Answer 1

C. From 0 to 4000 choose Old Process, From 4000 to infinity choose New Process

Step-by-step explanation:

Let the number of raft be denoted by Y

We are told that old process requires an investment of $4,000 and a variable cost of $6 per raft

Thus, old process cost is;

C_old = 4000 + 6Y

We are told that the new process has an investment of $20,000 and that the variable cost is $2 per raft..

Thus, new process cost is;

C_new = 20000 + 2Y

To find the volume demand by which each process will be chosen, we will equate both old and new costs to get;

4000 + 6Y = 20000 + 2Y

Rearranging, we have;

6Y - 2Y = 20000 - 4000

4Y = 16000

Y = 16000/4

Y = 4000

Thus, old process should be applied from 0 to 4000 and new process should be applied from 4000 to infinity.

Thus, option C is correct.