Marginal Profit Help: Find Production Level of 3000 Units per Month

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The marginal profit for a production level of 3000 units per month is $18.45. To find this, we can use the equation for marginal profit, which is given by p - C', where p is the price and C' is the derivative of the cost function. In this case, p = 20,000 - x/500 and C' = 9.55. Plugging in x = 3000, we get p - C' = (20,000 - 3000/500) - 9.55 = $20 - $9.55 = $18.45. In summary, the marginal profit for a production level of 3000 units per month is $18.45.
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scienceguy12
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Homework Statement



An electronics manufacturing company has determined that the cost of producing x units
of its newest personal stereo is given by C = 4000 + 9.55x, and the monthly demand
equation is given by px=20,000 - x/500. Find the marginal profit for a production level of
3000 units per month.

I know the answer is $18.45 but I can't figure out how to start. Would I take the deriv of C? Surely not...

Homework Equations





The Attempt at a Solution


I know the answer is $18.45 but I can't figure out how to start. Would I take the deriv of C? Surely not...
 
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Edit: I misread the question.
 

What is marginal profit?

Marginal profit is the additional profit gained from producing one more unit of a product. It takes into account the costs associated with producing that additional unit.

How is marginal profit calculated?

To calculate marginal profit, subtract the cost of producing one more unit from the revenue gained from selling that unit.

Why is it important to find the production level of 3000 units per month?

This production level is important because it helps determine the optimal level of production that will result in the highest marginal profit.

What factors affect marginal profit?

The main factors that affect marginal profit are the cost of production, the price of the product, and the demand for the product.

How can I increase marginal profit for 3000 units per month?

To increase marginal profit for 3000 units per month, you can try to reduce production costs, increase the selling price of the product, or improve marketing strategies to increase demand for the product.

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