Business Calculus Question

Question

Given the marginal revenue function dr/dq= (70e^q)+19-(q/24), find the demand function.

Step 1: Find the total revenue function, using the fact that there is no revenue when no units are sold.

r=

Step 2: Find the demand function when q>0, using the relation between price, demand, and revenue.

p=

Answer 1

Step 1. R(q) = ∫(70e^q) +19 - (q/24))dq = 70e^q + 19q - q²/48 + C; R(0) = 70 C = 0; C = - 70

R(q) = 70e^q + 19q - q²/48 - 70.

Step 2. R(q) = pq, q = R(q)/p