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”)

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.

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”) 

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.