Please help??? A manufacturer of tennis rackets finds that the totalcost C(x) (i

Question

Please help??? A manufacturer of tennis rackets finds that the totalcost C(x) (in dollars) of manufacturing "x" rackets/day isgiven by C(x) = 100 + 8x + 0.0001x^2. Each racket can be sold at a price of "p" dollars, where "p"is related to "x" by the demand equatiion p = 11 - 0.0004x If all rackets that are manufactured can be sold, find thedaily level of production that will yield a maximum profit for themanufacturer. ???? of rackets/day Please help??? A manufacturer of tennis rackets finds that the totalcost C(x) (in dollars) of manufacturing "x" rackets/day isgiven by C(x) = 100 + 8x + 0.0001x^2. Each racket can be sold at a price of "p" dollars, where "p"is related to "x" by the demand equatiion p = 11 - 0.0004x If all rackets that are manufactured can be sold, find thedaily level of production that will yield a maximum profit for themanufacturer. ???? of rackets/day

Explanation / Answer

A manufacturer of tennis rackets finds that the totalcost C(x) (in dollars) of manufacturing "x" rackets/day isgiven by C(x) = 100 + 8x + 0.0001x^2. Each racket can be sold at a price of "p" dollars, where "p"is related to "x" by the demand equatiion p = 11 - 0.0004x If all rackets that are manufactured can be sold, find thedaily level of production that will yield a maximum profit for themanufacturer. answer: if the number of rackets/day is x, cost per day = C(x) total sales per day = xp profit F per day = xp - C(x) to maximize F, we need dF/dx = 0 p + x dp/dx = dC/dx 11-.0004x + x ( -.0004) = 8 + .0002 x -.001 x = -3 x = 3000

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