This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Fresh day Senior, let's solve. Step 1: Determine the revenue function. The demand function is given by p = 40q. Revenue R is calculated as the product of price p and quantity q: R = p × q Substitute the given demand function into the revenue formula: R = (40q) × q R = 40q^2 Note: A typical demand function shows that price decreases as quantity increases. The given function p=40q implies that price increases with quantity, which is unusual for a demand function. Step 2: Analyze the revenue function for maximization. The revenue function is R(q) = 40q^2. This is a quadratic function representing a parabola that opens upwards. For production levels q 0, the value of R(q) continuously increases as q increases. To find a maximum, we would typically take the derivative and set it to zero: (dR)/(dq) = (d)/(dq)(40q^2) = 80q Setting (dR)/(dq) = 0 gives 80q = 0, which means q = 0. This corresponds to the minimum revenue (R=0), not a maximum. Since the function R(q) = 40q^2 increases indefinitely for q > 0, there is no finite maximum revenue. 1) At what level of production is revenue maximized? Based on the given demand function p=40q, the revenue function R(q) = 40q^2 continuously increases as the level of production q increases (for q 0). Therefore, there is no finite level of production at which revenue is maximized. Revenue can be made arbitrarily large by increasing production. No finite level of production 2) What is the maximum revenue at this point? Since there is no finite level of production that maximizes revenue, there is no finite maximum revenue. No finite maximum revenue Send me the next one 📸