Question

The weekly revenue R (in dollars) eamed by a computer repair service is given by R(p)=-14p^2+378p where p is the price charged per service hour (in dollars).

(a) Find the weekly revenues for prices per service hour of $12, $16, and $20. R(12)= $___ R(16)= $___ R(20)= $___
(b) Find the price that will yield a maximum weekly revenue. p =$ ___
(c) What is the maximum weekly revenue? R = $___

Answer 1

The weekly revenues for prices per service hour of $12, $16, and $20 are $2316, $2816, and $3120 respectively. The price that will yield a maximum weekly revenue is $13.50, and the maximum weekly revenue is $3267.

Step-by-step explanation:

To find the weekly revenues for prices per service hour of $12, $16, and $20, we need to substitute these values into the revenue function, R(p) = -14p^2 + 378p:

R(12) = -14(12)^2 + 378(12) = $2316
R(16) = -14(16)^2 + 378(16) = $2816
R(20) = -14(20)^2 + 378(20) = $3120

To find the price that will yield a maximum weekly revenue, we need to find the vertex of the quadratic equation. The price is given by the formula p = -b/(2a), where a = -14 and b = 378. Substituting these values, we get p = -378/(2(-14)) = 13.5. Therefore, the price that will yield a maximum weekly revenue is $13.50.

To find the maximum weekly revenue, we substitute the price into the revenue function: R(13.5) = -14(13.5)^2 + 378(13.5) = $3267.