Calculus Homework

Question

Given revenue and cost functions

Upper R left parenthesis q right parenthesis equals 70 q minus 0.5 q squaredR(q)=70q−0.5q2

and

Upper C left parenthesis q right parenthesis equals 13 q plus 500C(q)=13q+500​,

find the maximum profit that can be earned by selling this product.

Answer 1

Prpfit = revenue -cost so profit = 70q - q²/2 -( 13q +500) = 51q-q²/2 -500 to find the maximum profit take the derivative of the profit function wrt q or dP/dq =51 - q and to maximize set this to 0 so 51-q = 0 or q=51. Now go back to the profit equation and put the maximum value in to find the maximum profit. This gives 51²- 51²/2 -500 which equals 51²/2 -500 and P = $800.50