16) The revenue (in thousands of dollars) from producing x units of an item is modeled by
R(x) = 5x - 0.0005x2. Find the marginal revenue at x = 1000.

17) The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal
average cost function.

Question

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Respuesta :

calculista calculista · Answer 1 · 2019-10-08T11:02:35+02:00

Answer:

Part 16) The marginal revenue is $4,000

Part 17) The marginal average cost function is (70x+41)

Step-by-step explanation:

Part 16) we know that

The marginal revenue function is simply the derivative of the revenue function

we have

[tex]R(x)=5x-0.0005x^{2}[/tex]

Find [tex]\frac{dR(x)}{dx}[/tex]

[tex]R'(x)=5-0.001x[/tex]

For x=1,000 units

substitute

[tex]R'(x)=5-0.001(1,000)[/tex]

[tex]R'(x)=5-1=\$4[/tex]

Remember that the units is in thousands of dollars

therefore

The marginal revenue is $4,000

Part 17) we know that

The marginal average cost function is simply the derivative of the average cost function

we have

[tex]C(x)=(5x+3)(7x+4)[/tex]

Applying the distributive property

[tex]C(x)=35x^2+20x+21x+12[/tex]

[tex]C(x)=35x^2+41x+12[/tex]

Find the derivative

[tex]C'(x)=70x+41[/tex]

therefore

The marginal average cost function is (70x+41)