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The profit in dollars in producing $x$ -items of some commodity is given by the equation $P=-20 x^{2}+1300 x-15000 .$ To the nearest integer, how many items should be produced to (a) yield a profit of $\$ 2,000 ?$ (b) break even?

(a) 18,47(b) 15,50

Algebra

Chapter 0

Reviewing the Basics

Section 4

The Quadratic Formula and Applications

Equations and Inequalities

Missouri State University

Campbell University

Baylor University

Idaho State University

Lectures

02:52

The profit in dollars in p…

02:15

The revenue $R$, in dollar…

01:43

The profit, in thousands …

02:18

The total-cost and total-r…

01:56

Let $P(x)$ be the profit f…

02:33

02:55

The profit in dollars gene…

Yeah. In part a we just started a profit to 2000. And then we solve this quadratic equation. The first subtract the right hand side, both sides of their security which gives us 20 X squared miners serving 100 eggs. Class 15,000 plus 2000. It goes zero. And then we divide both sides by 20 which gives tax squared Minor 65 x. That's 850 it goes here. Now we can use the quadratic formula Here. A Echoes one. And the denominator is just too Vehicles minor 65. Any vehicles 65 miners square road out minor 65 squared minus four times one times It 150 So there's equals 65 plus um miners Five times the square root our 33/2. And if we use a calculator, The approximate value of these two solutions X one is approximately 18 and after two years, approximately 47 For part two, which is the start of the prophet to zero. Can resolve this quadratic equation. We divide both sides by -20 and then it gives us ax squared miners 65 ads because 752 0 and we can factor this quadratic creating And your two parts nature next minors 15 times. ErIC's my nerves. 50 it goes your and hence we get to solutions which are 15 yeah, 50. So don't know how to factor this quadratic equation. You can use a quadratic formula which will give you the same solutions.

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