Question

if the marginal cost of a product is 25+30x-9x^2 and the fixed cost is known to be 55, find the total cost where x indicates production output​

Answer 1

Answer:

25x + 15x² - 3x³ + 55

step-by-step explanation:

Let C(x) be the cost function.

Marginal cost is given by the change of C(x) with respect to x.

That is :

d/dx C(x) = Marginal cost.

Since we have been given the marginal cost we can get the cost function by integration.

We integrate the marginal cost.

Integrate 25 + 30x - 9x² = 25x + 30/2x² - 9/3x³

= 25x + 15x² - 3x³

This is the variable cost function.

Now the fixed cost = 55

Total cost = variable cost + fixed cost.

We sum this to get :

25x + 15x² - 3x³ + 55

This is the total cost.

Total cost = 25x + 15x² - 3x³ + 55