Don\'t understand how to solve part C. Please help me figure out the solution! A

Question

Don't understand how to solve part C. Please help me figure out the solution!

A manufacturer has been selling 1000 television sets a week at $300 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week. Round your answers to the nearest dollar. (a) Find the linear demand function (price as a function of units sold). rho (x) = 400 - x/10 (b) How large a rebate should the company offer the buyer in order to maximize its revenue? $ 100 (c) If the company experiences a cost of C (x) = 74,000 + 130x, how should the manufacturer set the size of the rebate in order to maximize its profit? $ 170

Explanation / Answer

Let x = the size of the rebate in dollars

Profit is revenue minus cost:
P(x) = R(x) - C(x)
P(x) = (-10x^2+2000x+300000) - (74,000 + 130x)
P(x) = -10x^2+1870x+226000
Take the derivative:
P'(x) = -20x + 1870
Set it equal to zero and solve:
-20x + 1870 = 0
x $93. 5

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