Question

The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x – 2x^2. For what number of tabletops does the company make a profit of $0?
100 tabletops
120 tabletops
240 tabletops
480 tabletops

Answer 1

Answer:

120 tabletops

Step-by-step explanation:

$p(x) = 480x - {2x}^{2} = 0 \\ p(120) = 480(120) - {2(120)}^{2} = 0 \\ p(120) = 57600 - {240}^{2} = 0 \\ p(120) = 57600 - 57600 = 0$

So,

120 tabletops will be the profit $0

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Answer 2

For 240 tabletops the company make a profit of $0

Solution:

Given that,

The profit a company makes from producing x tabletops is modeled by the equation:

$P(x) = 480x - 2x^2$

Where,

"x" is the number of laptops

From given,

P(x) = 0

Option A

100 tabletops

Put x = 100

$P(100) = 480(100) - 2(100)^2\\\\P(100) = 48000 - 20000\\\\P(100) = 28000$

Thus this option is wrong

Option B

120 tabletops

Put x = 120

$P(120) = 480(120) - 2(120)^2 \\\\P(120) = 57600 - 28800 \\\\P(120) = 28800$

Thus this option is wrong

Option C

240 tabletops

Put x = 240

P(240) = 480(240) - 2(240)^2\\\\

P(240) = 115200 -  115200

P(240) = 0

Thus this option is correct

Thus for 240 tabletops the company make a profit of $0

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