A product has a production cost function C(x)x and a revenue function R(x)x. Find and analyze the break-even quantity, then find the profit function.

A product has a production cost function C(x) =165x + 3630 and a revenue function R(x)= 220x. Find and analyze the break-even quantity, then find the profit function.

the break-even  quantity = 66

the profit function = 55x - 3630

Step-by-step explanation:

Given that:

C(x) = 165x + 3630

R(x) = 220 x

The Break-even quantity is C(x) = R(x)

∴

165x + 3630 = 220x

collecting the like terms, we have:

3630 = 220 x - 165 x

3630 = 55 x

x = 66

Thus, the break-even  quantity = 66

The profit function = R(x) - C(x)

The profit function = 220x - 3630 - 165x

By rearrangement

The profit function = 220x - 165x - 3630

The profit function = 55x - 3630