Revenue with calc

Question

The revenue from selling q items is R(q)=625q−q2, and the total cost is C(q)=50+6q. Write a function that gives the total profit earned, and find the quantity which maximizes the profit.

Answer 1

Hi Amanda,

 

Profit = Revenue - Cost

 

Profit = 625q - q² - 50 - 6q

 

Profit = 619q - q² -50

 

Now the Profit will have a maximum when the derivative is equal to zero

 

0 =619 -2q

 

619 = 2q

 

q = 309.5

 

the profit will be a maximum at 309 and 310

 

The maximum profit will be 95740

 

Hope this helps