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Sagot :

Answer:

[tex]P(x) = 16x - 100 - 0.1x^2[/tex]

Step-by-step explanation:

Given

[tex]R(x) = 46x[/tex]

[tex]C(x) = 100 +30x +0.1x^2[/tex]

Required

Determine the profit function

This is calculated as follows:

[tex]P(x) = R(x)- C(x)[/tex]

Substitute values for R(x) and C(x)

[tex]P(x) = 46x - (100 + 30x + 0.1x^2)[/tex]

Open bracket

[tex]P(x) = 46x - 100 - 30x - 0.1x^2[/tex]

Collect like terms

[tex]P(x) = 46x - 30x - 100 - 0.1x^2[/tex]

[tex]P(x) = 16x - 100 - 0.1x^2[/tex]