A company sells widgets.

Question

y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y=-30x^2+1325x-8569 y=−30x 2 +1325x−8569

Answer 1

IF y= price then profit or at least revenue = xy

xy = -30x^3 + 1325x^2 - 8569x

take the derivative and set it equal to zero to find the maximizing revenue level of output

-90x^2 + 2650x - 8569 = 0

90x^2 - 2650x = -8569

9x^ - 265x = -856.9

x = -265/18 +(1/18)sqr(265^2 +36(856.9)

ignore the negative square root

x = 2.94 = output for max profit (or min loss)

xy = revenue = 2.94(-30x^2+ 1325(x) - 8569 = $4,922.80 loss

the fixed cost is so high that no profit is possible. "Maximum profit" would be zero, by shutting down.

If the company stays open, it minimizes loss with 2.94 = x and has a loss of $4,922.80

$8569 is fixed cost which exceeds revenue for any output level