Question

Find the marginal profit funetion if cost and revenue tre giveri by C(x)=162+0.7x and R(x)=8x-0.06x^(2).

Answer 1

To find the marginal profit function, take the derivative of the revenue function and subtract the derivative of the cost function. In this case, the marginal profit function is -0.12x + 7.3.

Step-by-step explanation:

The marginal profit function can be found by taking the derivative of the revenue function with respect to the quantity produced and subtracting the derivative of the cost function with respect to the quantity produced. In this case, the revenue function is R(x) = 8x - 0.06x^2 and the cost function is C(x) = 162 + 0.7x. Taking the derivatives, we get R'(x) = 8 - 0.12x and C'(x) = 0.7. The marginal profit function is then given by P'(x) = R'(x) - C'(x). Simplifying, we have P'(x) = (8 - 0.12x) - 0.7 = -0.12x + 7.3.