Question

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.

Answer 1

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`