Find the revenue curve

Question

Use the equation y = -1/5x + 70 to find the revenue (R) in terms of P

Answer 1

P = -Q/5 + 70 with price measured on the y axis and quantity purchased on the x axis

Revenue= R(Q) = PQ = -Q^2/5 + 70Q = Revenue in terms of Q

to get Revenue in terms of Price, solve for Q

-Q/5 = P-70

Q = -5P + 350 and multiply by P

R(P) = PQ = -5P^2 + 350P

If you want the revenue maximizing price take the derivative and set = 0

R'(P) = -10P + 350

P=350/10 = 35