17) the total cost to produce x units of paint is c(x) = (5x + 3)(7x + 4). find the marginal
average cost function.

18) a company is planning to manufacture a new blender. after conducting extensive
market surveys, the research department estimates a weekly demand of 600 blenders at
a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per
blender. assuming the demand equation is linear, use the research department's
estimates to find the revenue equation in terms of the demand x.

17) MC(x) = 35 − 12/x²

18) R(x) = -0.05x² + 80x

Step-by-step explanation:

17) The marginal average cost function (MC) is the derivative of the average cost function (AC).

AC(x) = C(x) / x

MC(x) = d/dx AC(x)

First, find the average cost function:

AC(x) = C(x) / x

AC(x) = (5x + 3)(7x + 4) / x

AC(x) = (35x² + 41x + 12) / x

AC(x) = 35x + 41 + 12/x

Now find the marginal average cost function:

MC(x) = d/dx AC(x)

MC(x) = 35 − 12/x²

18) x is the demand, and p(x) is the price at that demand.  Assuming the equation is linear, let's use the points to find the slope:

m = (40 − 50) / (800 − 600)

m = -0.05

Use point-slope form to find the equation of the line:

p(x) − 50 = -0.05 (x − 600)

p(x) − 50 = -0.05x + 30

p(x) = -0.05x + 80

The revenue is the product of price and demand:

R(x) = x p(x)

R(x) = x (-0.05x + 80)

R(x) = -0.05x² + 80x

6.5

step-by-step explanation:

you said it was in the question

~courtney