So I haven't taken a math class in 10 years and I'm having some issues getting back into it. I'm hiring a private tutor, but in the mean time can someone help me with the below problem? I feel like it's pretty easy, I just can't figure out exactly what steps to take.
Suppose that x thousand units of a particular commodity are sold each month when the price is p dollars per unit, where p(x) = 5(24-x).
(a) Let E be the total monthly consumer expenditure, that is, the total amount of money consumers spend on this commodity in one month. Find a formula expressing E as a function of the price per unit.
(b) Sketch the graph of the function E(p).
(c) What market price produces the greatest total monthly consumer expenditure? How many units will be sold each month at this optimal price?
Suppose that x thousand units of a particular commodity are sold each month when the price is p dollars per unit, where p(x) = 5(24-x).
(a) Let E be the total monthly consumer expenditure, that is, the total amount of money consumers spend on this commodity in one month. Find a formula expressing E as a function of the price per unit.
(b) Sketch the graph of the function E(p).
(c) What market price produces the greatest total monthly consumer expenditure? How many units will be sold each month at this optimal price?