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The profit in dollars in producing $x$ -items of some commodity is given by the equation $P=-2 x^{2}+400 x-15000 .$ (a) How many items should be produced to break even? (b) How many items should be produced to maximize profit? (c) What is the maximum profit?

(a) $50,150(\text { b) } 100(\mathrm{c}) 5000$

Algebra

Chapter 0

Reviewing the Basics

Section 4

The Quadratic Formula and Applications

Equations and Inequalities

Campbell University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

02:49

The profit in dollars in p…

02:18

The total-cost and total-r…

02:50

01:56

The profit, in thousands …

01:43

Yeah Drinking even means they are the profit zero. So we just started a profit to zero. And we solve this quadratic a career first. We multiply both sides by miners are half. And this aquarium becomes Yeah squared Miners two hander eggs, class 7005 100. He called zero. We can factor this in korean into two terms which are parents minus 50 times. Acts 150 Ico zero. And so there are two solutions not sickles 50 or ax equals 150. If you don't know how to factor this quadratic equation, you can use a quadratic formula which will give you the same solutions for per B and percy. We first write the profit function has miners too. Tax squared Miners 200 x. Class 100 square And 100 squared is 10,000 -2 times 10,000 years, miners. 28,000. And therefore we should plus 20,000 hands in miners 15,000 Which Echoes -2 times. I had my nurses handler squared class 5000. Know that the square is always positive and there is a negative behind. Hence, this term is always negative zero. To yell at the maximum profits. This term should be zero and enhance when ex echoes a handwritten. The maximum profit is 5000.

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