17) The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginalaverage cost function.18) A company is planning to manufacture a new blender. After conducting extensivemarket surveys, the research department estimates a weekly demand of 600 blenders ata price of $50 per blender and a weekly demand of 800 blenders at a price of $40 perblender. Assuming the demand equation is linear, use the research department'sestimates to find the revenue equation in terms of the demand x.

Answer:17) MC(x) = 35 − 12/x²18) R(x) = -0.05x² + 80xStep-by-step explanation:17) The marginal average cost function (MC) is the derivative of the average cost function (AC).AC(x) = C(x) / xMC(x) = d/dx AC(x)First, find the average cost function:AC(x) = C(x) / xAC(x) = (5x + 3)(7x + 4) / xAC(x) = (35x² + 41x + 12) / xAC(x) = 35x + 41 + 12/xNow find the marginal average cost function:MC(x) = d/dx AC(x)MC(x) = 35 − 12/x²18) 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 = -0.05Use point-slope form to find the equation of the line:p(x) − 50 = -0.05 (x − 600)p(x) − 50 = -0.05x + 30p(x) = -0.05x + 80The revenue is the product of price and demand:R(x) = x p(x)R(x) = x (-0.05x + 80)R(x) = -0.05x² + 80x