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A fabrics company finds that the cost and​ revenue, in​ dollars, of producing x jackets is given by ​C(x)equals=940 plus 13 StartRoot x EndRoot940+13x and ​R(x)equals=83 StartRoot x EndRoot83x​, respectively. Determine the rate at which the fabric​ company's average profit per jacket is changing when 500500 jackets have been produced and sold.

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Given that a fabrics company finds that the cost and revenue, in dollars, of producing x jackets is given by

C(x)=940+13 √(x)
and

R(x)=83 √(x)
respectively.

The profit of the company from producing x jackets is given by P(x) = R(x) - C(x) =
83 √(x)-\left(940+13 √(x)\right)=70 √(x) -940

The rate at which the fabric company's average profit per jacket is changing is given by

(dP(x))/(dx) = (d)/(dx) (70 √(x) -940)= (35)/( √(x) )

Therefore, the the rate at which the fabric​ company's average profit per jacket is changing when 500 jackets have been produced and sold is given by

(35)/( √(x))= (35)/( √(500) ) =\$1.57
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