Question

Complex Analysis

6. A company is manufacturing smartphones at a cost of $100 per phone. They are trying to decide howto price their phones to maximize profit. Their market research suggests that, if they price the phones at $200 per phone, then they will sell 10,000 phones a month. For each $5 increase in price, the number of phones they will sell each month decreases by 400.

Naturally, the company hopes to maximize its monthly profit, so they've asked you to model the profit as a function of the price per phone. Here, we’ll help you by breaking this down into a few steps.

so we need to find the total revenue and total cost in terms of the price per phone. These obviously depend on the number of phones the company sells, so let's work on this first.

Write a formula for N(p), the number of phones the company will sell each month if they set the price per phone to p dollars.

) If the company sets the price per phone to p dollars, what is their total revenue each month?(This is the amount of money they make from selling phones.) Express your answer as a function of R.

=) If the company sets the price per phone to p dollars, how much will it cost them to manufacture the number of phones they'll sell each month?

O Express the company's monthly profit as a function of p.

(e) Suppose the original problem was changed slightly to the following (only the highlighted part is different):

A company is manufacturing smart phones at a cost of $100 per phone. They are trying to decide how to price their phones to maximize profit. Their market research suggests that, if they price the phones at $200 per phone, then they will sell 10,000 phones a month. For each $5 increase in price, the number of phones they will sell each month decreases by 10%.


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