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Quadratic Model: Completing the Square to Solve a Maximum Profit Question

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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?

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Solution Summary

Completing the Square to Solve a Maximum Profit Question is investigated. The solution is detailed and well presented.

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The profit expression P(x) = - x2 + 120x can be rewritten as:
P(x) = - x2 + 120x
= - (x2 - 120x)
= - (x2 - 120x + 3600 - 3600)
= - (x2 ...

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