Profit

[TheNextOne]

A computer manufacturer sells 2,000 laptops per month at a profit of $300 per
unit. Market research indicates that for each $10 factory rebate offered to customers, it is expected that 100 more laptops will be sold per month. How much of a rebate should be offered in order to maximize the monthly profit? What is the maximum monthly profit?

I am having difficulty with this problem.

This is what i have so far:
P=TR-TC
TR= pq
p= (y- 10x)
q= (2000 + 100x)

I cant seem to figure out the beginning price or the total cost. If someone could help me with that, i could do the rest by myself.

 

[galactus]

Let x be the number of $10 rebates.

\(\displaystyle (2000+100x)(300-10x)\)

differentiate, set to 0, solve for x.

 

[TheNextOne]

Are u sure that the begnning price is 300 per unit? I assumed that that was the profit per unit. What about the total cost? Thank you!

 

[stapel]

Are u sure that the begnning price is 300 per unit?

The text of the exercise (as posted) does not provide the selling price, only the amount of the profit. Since the exercise relates profit, units, and rebates, I'm not sure why you're saying the actual list price is needed...?

Eliz.