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September 23, 2014

September 23, 2014

Posted by **jen** on Tuesday, April 7, 2009 at 2:45pm.

P=$35-0.02Q where P=selling price/unit and Q=quantity sold/unit.

on the other hand, management estimates that the average cost of manufacturing and sellling the product will decrease as the quantity sold increases. they estimate:

C=$4Q+$8000.

where C=cost to produce and sell Q/year.

The firm's management wishes to produce and sell the product at the rate that will maximize profit, that is, income minus cost will be a maximum. what quantity should the decision makers plan to produce and sell each year.

I know the answer is 775 units and i have to take derivatives of something because it's asking for a maximum, but how do i put the two equations together.

- economics -
**economyst**, Wednesday, April 8, 2009 at 9:33amThis is a classic maximize-profits for a monopolist. Always, always, always, maximize where marginal cost (MC) equals marginal revenue (MR).

OK, Total Revenue is P*Q. Using your demand equation TR=35Q-.02Q^2. Marginal revenu is the first derivitive of total revenue, so MR=35-.04Q

Marginal cost is the first derivitive of total cost, so TC = 4.

Maximized profits occur when MC=MR or 4 = 35-.04Q. Solve for Q. (I get 775)

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