The variable cost for the production of a calculator is $13.75 and the initial investment is $210,000.Use differentials to approximate the change in the cost C for a one-unit increase in production when ,where x is the number of units produced.
A) 687,500.00 dollars
B) 14.75 dollars
C) 688,500.00 dollars
D) 13.75 dollars
E) 23.75 dollars

Question

The variable cost for the production of a calculator is $13.75 and the initial investment is $210,000.Use differentials to approximate the change in the cost C for a one-unit increase in production when  ,where x is the number of units produced. ​
A) ​687,500.00 dollars 
B) ​14.75 dollars 
C) ​688,500.00 dollars 
D) ​13.75 dollars 
E) ​23.75 dollars

Quizplus · Accepted Answer

We can use the formula for differentials:

dC = C'(x)dx

where C'(x) is the derivative of the cost function with respect to x, and dx is the change in x.

Since the variable cost is constant, the cost function is:

C(x) = 13.75x + 210000

Taking the derivative with respect to x, we get:

C'(x) = 13.75

Therefore, the differential is:

dC = 13.75 dx

For a one-unit increase in production, dx = 1, so:

dC = 13.75 dollars

Therefore, the best choice is D, since it is the only option that matches the calculated differential.

The Variable Cost for the Production of a Calculator Is