How do I answer these?

Question

The demand function for a good is p=49−0.04q. Round your numeric answers to one decimal place. a) Write the revenue as a function of production, q. R(q) =

b) What production level maximizes revenue? q =

c) What price corresponds to this production level? price = $

d) What is the total revenue at this production level? revenue = $

Answer 1

p = 49 - 0.04q

R(q) = pq = 49q - 0.04q^2

R'(q) = 49 -0.08q = 0

q = 49/.08 = 612.5 is the revenue maximizing production level

p = 49-0.04(612.5) = 49 - 24.5 = $24.50 = revenue maximizing price

R(612.5) = 49(612.5)- 0.04(612.5)^2 = $15,006.25

or max R = pq = 24.5(612.5) = $15,006.25 = maximum revenue