The next questions refer to the following.
Consider the following production function for a delivery service.

Each delivery generates $200 in gross revenue, and the tax rate is 10 percent on profits. Each truck costs $11,000.
-The optimal number of trucks is
A) 1
B) 2
C) 3
D) 4
E) 5

Question

The next questions refer to the following.
Consider the following production function for a delivery service.

Each delivery generates $200 in gross revenue, and the tax rate is 10 percent on profits. Each truck costs $11,000.
-The optimal number of trucks is
A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Quizplus · Accepted Answer

To find the optimal number of trucks, we need to look for the point where the marginal cost of adding an additional truck is equal to the marginal revenue generated by that truck. In other words, we need to find the point where the derivative of the total profit function with respect to the number of trucks is equal to zero.

Taking the derivative of the profit function with respect to the number of trucks and setting it equal to zero, we get:

-11,000 + 200(4.4x - 4.4x^2) = 0

Solving for x, we get x = 0.5, 1.5, and 2.5. Since we can't have a non-integer number of trucks, the optimal number of trucks is 3.

Adding a fourth truck would decrease profits because the marginal cost would exceed the marginal revenue. Therefore, the best choice is to have 3 trucks.

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