Suppose a product's revenue function is given by R ( q ) = − 3 q 2 + 900 q , where R ( q ) is in dollars and q is units sold. Also, it's cost function is given by C ( q ) = 174 q + 33750 , where C ( q ) is in dollars and q is units produced. Find a simplified expression for the item's Marginal Profit function ( M P ( q ) ) and record your answer in the box. Be sure to use the correct variable. (Use the Preview button to check your syntax before submitting your final result). Answer: M P ( q ) = LicensePoints possible: 1 Unlimited attempts. Message instructor about this question

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-07-31T14:04:02+02:00

Answer:

The required marginal profit function is: [tex](MP(q))=-6q+726[/tex]

Explanation:

The marginal profit is the profit earned by producing one extra unit of the product.

The revenue function is [tex]R(q)=-3q^2+900q[/tex]

The cost function is [tex]C(q)=174q+33750[/tex]

The profit function is [tex]P(q)=R(q)-C(q)[/tex]

[tex]\implies P(q)=-3q^2+900q-(174q+33750)[/tex]

[tex]\implies P(q)=-3q^2+900q-174q-33750[/tex]

[tex]\implies P(q)=-3q^2+726q-33750[/tex]

The marginal profit is the derivative of the profit function.

[tex]\implies (MP(q))=-6q+726[/tex]

Therefore the required marginal profit function is: [tex](MP(q))=-6q+726[/tex]

andromache andromache · Answer 2 · 2022-02-24T16:30:55+01:00

The required marginal profit function is (M P(q)) = -6q + 726.

Since the marginal profit should be profit earned by generating one extra unit of the product.

Now

The revenue function is [tex]R ( q ) = - 3 q^2 + 900 q[/tex]

Now the cost function is C ( q ) = 174 q + 33750

And, the profit function is P(q) = R(q) - C(q)

So,

[tex]= -3q^2 + 900q - (174q + 33750)\\\\= -3q^2 + 900q - 174q - 33750\\\\= -3q^2 + 726q - 33750[/tex]

Now the profit function is (M P(q)) = -6q + 726.

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