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 phonesat$200 per phone, then they will sell 10,000 phones a month. For each$5 increase in price, the numberof 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 profitas a function of the price per phone. Here, we'll help you by breaking this down into a few steps.(a) First,profit = (total revenue)(total cost),so we need to find the total revenue and total cost in terms of the price per phone. These obviouslydepend on the number of phones the company sells, so let's work on this first.Write a formula forN(p), the number of phones the company will sell each month if they set theprice per phone topdollars.(b) If the company sets the price per phone topdollars, what is their total revenue each month?(This is the amount of money they make from selling phones.) Express your answer as a functionofp.(c) If the company sets the price per phone topdollars, how much will it cost them to manufacturethe number of phones they'll sell each month?(d) Express the company's monthly profit as a function ofp.(e) Suppose the original problem was changed slightly to the following (only the highlighted part isdifferent):2

A company is manufacturing smartphones at a cost of$100 per phone. They are tryingto decide how to price their phones to maximize profit. Their market research suggeststhat, if they price the phones at$200 per phone, then they will sell 10,000 phones amonth. For each$5 increase in price, the number of phones they will sell each monthdecreases by10%.Express the company's monthly profit (in this new scenario) as a function ofp, the price perphone in dollars.