Steve owns a bakery. He has hired a consultant to analyze his business operations, and the consultant has told him that his profits from the sale of pies is given by the following function:
P(x) = 120x - x2
where P(x) is the profit and x refers to the number of pies baked.
(a) How many units of pies should Steve bake in order to maximize profits?
(b) What is the maximum profit Steve can make?
The profit expression P(x) = - x2 + 120x can be rewritten as:
P(x) = - x2 + 120x
= - (x2 - 120x)
= - (x2 - 120x + 3600 - 3600)
= - (x2 ...
Completing the Square to Solve a Maximum Profit Question is investigated. The solution is detailed and well presented.