Question

The total cost of producing a type of boat is given by C(x)=22000−40x+0.02x2

, where x is the number of boats produced. How many boats should be produced to incur minimum cost?

Answer 1

To find the number of boats that should be produced to incur minimum cost, we need to find the value of x that minimizes the cost function C(x).

We can do this by taking the derivative of the cost function with respect to x, setting it equal to zero, and solving for x.

C(x) = 22000 - 40x + 0.02x^2

C'(x) = -40 + 0.04x

Setting C'(x) = 0, we get:

-40 + 0.04x = 0

0.04x = 40

x = 1000

Therefore, the number of boats that should be produced to incur minimum cost is 1000.

Explanation: