Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 7

Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering massproducing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be $25,000, while labor, materials, packaging, and shipping will be about $10 per doll. He has determined that sales volume is related to price, according to the following linear equation:
v = 4,000 - 80 p
Develop the nonlinear profit function for Andy and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.