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Sagot :
Given:
The cost function is
[tex]C(x)=7x[/tex]
The revenue function is
[tex]R(x)=9x-0.001x^2[/tex]
To find:
The marginal cost, marginal revenue, and marginal profit functions.
Solution:
We know that,
[tex]Profit=Revenue-Cost[/tex]
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=9x-0.001x^2-7x[/tex]
[tex]P(x)=2x-0.001x^2[/tex]
The marginal cost, marginal revenue, and marginal profit functions are the derivatives of cost, revenue and profit functions respectively.
Marginal cost function is
[tex]C'(x)=7\dfrac{d}{dx}x[/tex]
[tex]C'(x)=7(1)[/tex]
[tex]C'(x)=7[/tex]
Marginal revenue function is
[tex]R'(x)=9(1)-0.001(2x)[/tex]
[tex]R'(x)=9-0.002x[/tex]
Marginal profit function is
[tex]P'(x)=2(1)-0.001(2x)[/tex]
[tex]P'(x)=2-0.002x[/tex]
Therefore, the marginal cost, marginal revenue, and marginal profit functions are [tex]C'(x)=7[/tex], [tex]R'(x)=9-0.002x[/tex] and [tex]P'(x)=2-0.002x[/tex] respectively.
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