Posted by **Sarah** on Monday, March 25, 2013 at 2:52pm.

The monthly demand function for a product sold by a monopoly is

p = 3750 − 1/3x^2 dollars, and the average cost is C = 1000 + 70x + 3x^2

dollars. Production is limited to 1000 units and x is in hundreds of units.

(a) Find the quantity that will give maximum profit.

(b) Find the maximum profit. (Round your answer to the nearest cent.)

- Calculus - Incomplete -
**Steve**, Monday, March 25, 2013 at 2:57pm
profit = revenue - cost

revenue = price * quantity

cost = avg cost * quantity

No indication is given regarding price per unit.

- Calculus -
**Sarah**, Monday, March 25, 2013 at 3:33pm
I've done p= x(3750 − 1/3x^2) and C = x(1000 + 70x + 3x^2)

Profit= 3750x-1/3x^3-1000x-70x^2-3x^3= 2750x-70x^2-4/3x^3

P'(x)= 2750-140x-12x^2

Then I did the Quadratic Formula and and got 22 but it's wrong

- Calculus -
**Steve**, Monday, March 25, 2013 at 5:07pm
There seems to be something wrong here.

It appears that x is the selling price, making

x(3750 − 1/3x^2) the revenue

But how can the average cost C be dependent on the selling price?

Are you somehow mixing up x, making it the price in one place and the quantity in another?

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