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). m p ( q ) = licensepoints possible: 1 unlimited attempts. message instructor about this question

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

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

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

So,

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

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The required marginal profit function is:

Explanation:

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

The revenue function is

The cost function is

The profit function is

The marginal profit is the derivative of the profit function.

Therefore the required marginal profit function is:

a.