To calculate: The break-even point for P(x)=-1100+120x-x^{2}

Harold Kessler 2021-12-16 Answered
To calculate: The break-even point for
P(x)=1100+120xx2
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Expert Answer

Suhadolahbb
Answered 2021-12-17 Author has 32 answers
Step 1
Given Information:
Profit function, P(x)=1100+120xx2
Formula Used:
Break-even point is the point, when profit is zero or revenue is equal to the cost.
Profit=Total revenueTotal cost
Zero product property:
The General form of quadratic equation is ax2+bx+c=0
Where a, b, c are constants and a0
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(x)=0
1100+120xx2=0
x2110x10x+1100=0
Take the common terms outside the parenthesis
x(x110)10(x110)=0
(x10)(x110)=0
Use the zero product property,
x10=0 or x110=0
x=10 or x=110
It is given that x100
Hence, the break-even point is 10 units.

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Esta Hurtado
Answered 2021-12-18 Author has 39 answers

Step 1
P(x)=1100+120xx2
Quadratic polynomial can be factored using the transformation
ax2+bx+c=a(xx1)(xx2)
where x1 and x2 are the solutions of the quadratic equation
ax2+bx+c=0
x2+120x1100=0
All equations of the form ax2+bx+c=0 can be solved using the quadratic formula: b±b24ac2a. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=120±12024(1)(1100)2(1)
Square 120
x=120±144004(1)(1100)2(1)
Multiply -4 times -1
x=120±14400+4(1100)2(1)
Multiply 4 times -1100
x=120±1440044002(1)
Add 14400 to -4400
x=120±100002(1)
Take the square root of 10000
x=120±1002(1)
Multiply 2 times -1
x=120±1002
Now solve the equation x=120±1002 when ± is plus
Add -120 to 100
x=202
Divide -20 by -2
x=10
Now solve the equation x=120±1002 when ± is minus
Subtract 100 from -120
x=2202
Divide -220 by -2
x=110
Factro the original expression using ax2+bx+c=a(xx1)(xx2). Substitute 10 for x1 and 110 for x2
x2+120x1100=(x10)(x110)

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