Question

Marginal Revenue: Gardenscapes finds that its monthly revenue, in dollars, from the sale of x carved stone fountains is given by R(x)=0.62x3−7.4x2+2510x a) What is the revenue earned from selling 85 fountains? b) Find the marginal revenue function. c) Determine the marginal revenue when 85 fountains are sold. d) Use the answers from parts (a) and (c) to estimate the revenue that would result in selling 86 fountains this month.

Answer 1

To find the revenue earned from selling 85 fountains, substitute x=85 in R(x). The marginal revenue function is the derivative of R(x). The marginal revenue when 85 fountains are sold can be found by substituting x=85 in MR(x). To estimate the revenue from selling 86 fountains, substitute x=86 in R(x).

Step-by-step explanation:

a) To find the revenue earned from selling 85 fountains, we can substitute x=85 in the revenue function R(x)=0.62x^3−7.4x^2+2510x. Evaluating the expression, we get R(85) = 0.62(85)^3 - 7.4(85)^2 + 2510(85).

b) The marginal revenue function can be found by taking the derivative of the revenue function with respect to x. So, the marginal revenue function is given by MR(x) = 3(0.62x^2) - 2(7.4x) + 2510.

c) The marginal revenue when 85 fountains are sold can be found by substituting x=85 in the marginal revenue function MR(x) = 3(0.62x^2) - 2(7.4x) + 2510.

d) We can estimate the revenue that would result in selling 86 fountains by substituting x=86 in the revenue function R(x)=0.62x^3−7.4x^2+2510x. Evaluating the expression, we get R(86) = 0.62(86)^3 - 7.4(86)^2 + 2510(86).