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= 3750x1/3x^31000x70x^23x^3= 2750x70x^24/3x^3
P'(x)= 2750140x12x^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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