Probably very easy question

bthegreat

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Jan 15, 2019
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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?
 
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?

(a) How is E related to p (the price of one unit) and x (the number of thousand units sold)? One tricky point here: they give p as a function of x, but you'll have to rewrite that to show x as a function of p, since they want E(p), not E(x).

(b) You could just plot some points, or use knowledge from the past about this type of equation (it will be quadratic). Or, for now, enter it into a graphing program like desmos.com and see if that makes it look familiar.

(c) Tell us what you know about finding the maximum of a function, or use information you found in graphing.

To give better help, we'll want to know what you do know, so we can be sure to be understood. The more you tell us of your own thinking, the quicker we can help.
 
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