profit is revenue minus cost, or
x*p(x) - c(x)
= x(18-x/400)-(820+5x+0.01x^2)
= -0.0125x^2 + 13x - 820
That's just a parabola, with its vertex at x = -b/2a = 520
work #2 the same way. Figure a quantity and a price in terms of x, the number of $10 rebates. Then, revenue is price*quantity.
1. For the given cost and demand functions, find the production level that will maximize profit.
C(x)=820+5x+0.01x^2, p(x)=18-x/400. Find the answer to the nearest whole number.
a. x = 538
b. x = 525
c. x = 511
d. x = 520
2. A manufacturer has been selling 1,100 television sets a week at $450 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. How large a rebate should the company offer the buyer in order to maximize its revenue?
Select one:
a. $127.50
b. $85.00
c. $170.00
d. $340.00
1 answer