How Can Terrific Wears Inc. Maximize Revenue and Profit from Suit Sales?

[melissa1456]

Terri c Wears Inc., a clothing rm determines that the demand for their suits is given by d = 2(175􀀀p),
where d represents the demand and p represents the price of a suit. (Recall that Revenue=PriceDemand,
Profi t=Revenue-Cost.)
(1) Find the selling price for a suit that will generate maximum revenue.

(2) How many suits are likely to be sold at that price in (1)?

(3) What is the maximum revenue?
Additional research shows that the cost of producing x suits is given by: C(x) = 350 + 0:75x.

(4) Find an expression which will determine the pro t the company would make on selling x suits.(5) Determine the number of suits that the company must produce and sell in order to make maximum
pro t.

(6) Determine that maximum profi t.

(7) At what price should a suit be sold in order to maximize profi t?

 

[MarkFL]

Hello and welcome to MHB, melissa1456! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

Also, can you explain the following: d = 2(175􀀀p)

 

[melissa1456]

Hello and welcome to MHB, melissa1456! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

Also, can you explain the following: d = 2(175􀀀p)

So d=2(175-p) is the equation in order to get the demand. I am currently stuck and don't know how to begin question #1.

 

[MarkFL]

Okay, revenue $R$ is price per unit times units sold, or demand, so we may state:

\(\displaystyle R=p\cdot d=2p(175-p)\)

Now, in this factored form, we see that revenue is a quadratic in $p$, opens downward, and so its maximum will occur on its axis of symmetry, which will be midway between the two roots. Can you identify the two roots of the revenue function?