A company models its net income, in thousands of dollars, with the function f(x)=9x2−54x−144 , where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?

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MrRoyal MrRoyal · Answer 1 · 2022-01-04T11:41:15+01:00

The company needs to sell 8 units in order for the net income to equal $0

The net income function is given as:

[tex]f(x) = 9x^2 - 54x - 144[/tex]

When the net income is 0, then f(x) = 0.

So, we have:

[tex]9x^2 - 54x - 144 = 0[/tex]

Divide through by 9

[tex]x^2 - 6x - 16 = 0[/tex]

Expand the above equation

[tex]x^2 +2x- 8x - 16 = 0[/tex]

Factorize the above equation

[tex]x(x +2)- 8(x + 2) = 0[/tex]

Factor out x + 2 in the above equation

[tex](x - 8)(x + 2) = 0[/tex]

Split and solve for x

[tex]x = 8[/tex] or [tex]x =-2[/tex]

The units of product cannot be negative.

So, the value of x is [tex]x = 8[/tex]

Hence, the company needs to sell 8 units

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