Question

You want to sell a certain number n of items in order to maximize your profit. Market research tells you that if you set the price at $1.50, you will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50 you will be able to sell another 1000 items. Suppose that your fixed costs (“start-up costs”) .

Answer 1

this is what i got so far:
r(x)=nx---> revenue for selling n items at x dollars
c(x)=2000+0.5n ---> cost
n(x)=5000 + 1000(1.5- 0.10x)
these are my equations, i calculated it until the end, but i got wrong answer. i got x=1.55 or x=33.95 but the right answer is x=1.25

Answer 2

What happened to your fixed costs?

Answer 3

oopss.. the problem should be like this:

You want to sell a certain number n of items in order to
maximize your profit. Market research tells you that if you set the price at
$1.50, you will be able to sell 5000 items, and for every 10 cents you lower
the price below $1.50 you will be able to sell another 1000 items. Suppose
that your fixed costs (“start-up costs”) total $2000, and the per item cost of
production (“marginal cost”) is $0.50. Find the price to set per item and the
number of items sold in order to maximize profit, and also determine the
maximum profit you can get.