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Let​ R(x), C(x), and​ P(x) be,​ respectively, the​ revenue, cost, and​ profit, in​ dollars, from the production and sale of x items. If ​R(x) equals = 6 6x and ​C(x) equals = 0.004 x squared plus 2.3 x plus 50 0.004x2+2.3x+50​, find each of the following. ​a)​ P(x)

Answer :

Answer:

[tex]P(x) = -0.004x^2 - 3.7x - 50[/tex]

Step-by-step explanation:

We have to find profit [tex]P(x)[/tex].

This can be easily found using a formula for Profit given the Revenue and Cost.

[tex]Profit = Revenue - Cost[/tex]

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

Given that:

[tex]R(x) = 6x[/tex]

[tex]C(x) = 0.004x^2 + 2.3x + 50[/tex]

to find P(x) we can simply subtract R(x) by C(x).

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

[tex]P(x) = (6x) - (0.004x^2 + 2.3x + 50)[/tex]

[tex]P(x) = 6x - 0.004x^2 - 2.3x - 50[/tex]

and finally, after simplify this equation subtracting 6x by 2.3x.

this is the equation for the profit [tex]P(x)[/tex]

[tex]P(x) = -0.004x^2 - 3.7x - 50[/tex]

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