The demand equation for a certain commodity is given by the following equation. 1 p = x² – 6x + 108, Osx<36 12 Find x and the corresponding price p that maximize revenue. The maximum value of R(x) occurs at x =

A supply company charges for 90-liter drums using the demand function p(x)=20.9−1.6x  What is the revenue function?

4. It costs C(x) = 112 + 1.4x dollars to produce x Specialty Hair Ribbons. To sell x Specialty Hair Ribbons, the price should be set at p(x) = 18 - 0.2x. a.Find the revenue function R(x) and the profit function P(x) when the manufacturer makes and sells x ribbons. Simplify your functions. R(x) P(x) b. How many ribbons should be made and sold to break even? Round your answers) to the nearest whole number and include units. What profit (or loss) does the manufacture incur when they make and sell 32 ribbons? Circle profit or loss and fill in the blank below rounding to the nearest whole dollar. At a production level of 32 Ribbons, they have a profit / 1OSS of

A company can manufacture at most 200 units per month. About x units per month can be sold at the price p(x) = (500 – x) dollars and the cost of producing x units per week is C(x) = 150 + 4x + x2 dollars. Find; a. Revenue from sale of x units per week b. Maximum weekly profit and the number of units produced to obtain the maximum d. Marginal Revenue at Maximum weekly profit level c. Marginal cost functions at Maximum weekly profit level