1. Spring Time Manufacturers produces a single product and the
company is trying to determine the effectiveness of their
pricing decisions. As a consultant, you have been asked to
develop cost functions that will assist in arriving at the
optimal price that will enable the company to maximize
profits. During the year, you were provided with the following
demand and costs functions for the product:
P = 485-25Q, where P is the unit selling price and Q is quantity
of units in thousands.
TC = 5Q² +95Q + 200, where TC is total costs in thousands of
dollars.
Required:
(a) Find the output at which profit is maximized.
(b) Find the optimal price that maximizes profit.
(c) Determine the optimal sales revenue.
(d) Calculate the maximum profit.