SOLUTION: Please help me to solve this problem. The demand equation for a manufacturer's product is {{{p=(80-q)/4}}}, 0 ≤ q ≤ 80 , where q is the number of units and p is the pri
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Question 465289: Please help me to solve this problem. The demand equation for a manufacturer's product is , 0 ≤ q ≤ 80 , where q is the number of units and p is the price per unit. At what value of q will there be the maximum revenue? What is the maximum revenue?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assuming all the economic demand is met and q items are sold, the amount of revenue will be pq, or
 = -\frac{q^2}{4} + 20q)
This is a quadratic opening downward, so the maximum revenue occurs at the "vertex" or at q = -20/(-1/2) = 40 (also halfway between 0 and 80). The revenue will be
 = 400)
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