The demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. p = −0.01x2 − 0.1x + 45   Determine the consumers' surplus if the market price is set at $3/cartridge. (Round your answer to two decimal places.)

Find the consumers’ surplus at a price level of ?̅= $150 for the price demand equation ?(?) = 400 − 0.05?

The scrap value of a machine at the end of its useful life is given by S(n) = C(1-r)", where C is the original cost, n is the useful life of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine. Original cost, $49,000; life, 11 years; annual rate of value lost, 13% S=$ (Round to the nearest cent.)

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