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.

solve the above engineering problem using calculus.

hints: 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.

to achieve m3, you must present your work using coherent, logical development of principles/concepts in determining the maximum profit and use technical language accurately.
to achieve d1, you must evaluate the validity of your answer using the given data.