Harold Kessler

2021-12-16

To calculate: The break-even point for

$P\left(x\right)=-1100+120x-{x}^{2}$

Suhadolahbb

Beginner2021-12-17Added 32 answers

Step 1

Given Information:

Profit function,$P\left(x\right)=-1100+120x-{x}^{2}$

Formula Used:

Break-even point is the point, when profit is zero or revenue is equal to the cost.

$\text{Profit}=\text{Total revenue}-\text{Total cost}$

Zero product property:

The General form of quadratic equation is$a{x}^{2}+bx+c=0$

Where a, b, c are constants and$a\ne 0$

For real numbers a and b.$ab=0$ if and only if $a=0$ or $b=0$ or both.

Step 2

Calculation:

To find the break-even point, put revenue is equal to the cost.

$P\left(x\right)=0$

$-1100+120x-{x}^{2}=0$

${x}^{2}-110x-10x+1100=0$

Take the common terms outside the parenthesis

$x(x-110)-10(x-110)=0$

$(x-10)(x-110)=0$

Use the zero product property,

$x-10=0$ or $x-110=0$

$x=10$ or $x=110$

It is given that$x\le 100$

Hence, the break-even point is 10 units.

Given Information:

Profit function,

Formula Used:

Break-even point is the point, when profit is zero or revenue is equal to the cost.

Zero product property:

The General form of quadratic equation is

Where a, b, c are constants and

For real numbers a and b.

Step 2

Calculation:

To find the break-even point, put revenue is equal to the cost.

Take the common terms outside the parenthesis

Use the zero product property,

It is given that

Hence, the break-even point is 10 units.

Esta Hurtado

Beginner2021-12-18Added 39 answers

Step 1

Quadratic polynomial can be factored using the transformation

where

All equations of the form

Square 120

Multiply -4 times -1

Multiply 4 times -1100

Add 14400 to -4400

Take the square root of 10000

Multiply 2 times -1

Now solve the equation

Add -120 to 100

Divide -20 by -2

Now solve the equation

Subtract 100 from -120

Divide -220 by -2

Factro the original expression using

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