Question

The monthly revenue of a certain company is given by R 820p-7p, where p is the price in dollars of the product the company manufactures. At what price will the revenue be $12,000 if the price must be greater than $50? $ The revenue will be $12,000 when the price of the product is (Simplify your answer.)

Answer 1

The revenue will be 12,000 when the price of the product  is $100

Given :

The monthly revenue of a certain company

$R=820p-7p^2$

We need to find out p when Revenue R is 12000

Lets replace R with 12000 and solve for p

$12000=820p-7p^2\\820p-7p^2=12000\\-7p^2+820p-12000=0$

Apply quadratic formula

$p=\frac{-820\pm \sqrt{820^2-4\left(-7\right)\left(-12000\right)}}{2\left(-7\right)}\\p=\frac{-820\pm \:580}{2\left(-7\right)}\\p=\frac{-820+580}{2\left(-7\right)},\:p=\frac{-820-580}{2\left(-7\right)}\\p=\frac{120}{7},\:p=100$

Given that price must be greater than 50

So the revenue will be 12000 when the price of the product  is $100

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