A marketing researcher has determined that when a product sells at x dollars per unit' the number of units sold per week is given by the function

q= 75/x-m + 80(5m -x)

where m > 0 is the total manufactunng cost in dollar per unit and m < x <5m.

(a) Find the profit function P(x) (in dollars per week) and simplify it.

(b) Use calculus to find the selling price x that maximizes weekly profit. Sufficiently justify your solution

(c) Use your answer to part (b) to determine the manufacturing cost m that yields a maximum weekly profit of 3,455 dollar

thanks