1. ## Word Problem

Not sure what I am doing wrong..

Question:

Terry makes and sells necklaces. He has observed over time that when the price is $9 each, he sells an average of 30 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost$8. Express his profit P as a function of x, the number of necklaces sold.

What I have:

Profit function is revenue minus cost. Thus:

P(x)=R(x)-C(x)

And R(x)= P*Q Where P is Price and Q is quantity.

My Formula:

$(9+x)(30-3x)-8(30-3x)$
Simplify:
$-3x^2+27x+30$

What am I missing?

2. mvho!

Terry makes and sells necklaces.
He has observed over time that when the price is $9 each, he sells an average of 30 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost$8.
Express his profit P as a function of x, the number of necklaces sold.

What I have:

Profit function is Revenue minus Cost: .$\displaystyle P(x)\:=\:R(x)-C(x)$

And $\displaystyle R(x)\:=\:P\cdot Q$ where $\displaystyle P$ is Price and $\displaystyle Q$ is Quantity.

My formula: .$\displaystyle P(x) \:=\:(9+x)(30-3x) - 8(30-3x)$ . . . . Correct!

Simplify: .$\displaystyle P(x) \:=\:-3x^2 + 27x + 30$ .??

What am I missing? . . . . some arithmetic?

You had: .$\displaystyle P(x) \:=\:(9+x)(30-3x) - 8(30-3x)$

. . . . . . . . . . .$\displaystyle = \;270 \;{\color{red}-\;27x} + 30x - 3x^2 - 240 \;{\color{red}+\;24x}$

. . . . . . . . . . .$\displaystyle = \;-3x^2 \;{\color{red}-\;3x} + 30$

3. LOL

That's actually the answer I had previously also but its not accepting neither. I don't see how you get -3x as opposed to 27x though. Because you have -27x+30x+24x=27x?

So I am thinking it is my formula. Maybe I should be expressing "X" as something else?

Did I do this part correctly at least?

"Express his profit P as a function of x, the number of necklaces sold."

4. Hello mvho
Originally Posted by mvho
Not sure what I am doing wrong..

Question:

Terry makes and sells necklaces. He has observed over time that when the price is $9 each, he sells an average of 30 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost$8. Express his profit P as a function of x, the number of necklaces sold.

What I have:

Profit function is revenue minus cost. Thus:

P(x)=R(x)-C(x)

And R(x)= P*Q Where P is Price and Q is quantity.

My Formula:

$(9+x)(30-3x)-8(30-3x)$ No. In this formula, x represents the number of dollars price increase.
Simplify:
$-3x^2+27x+30$

What am I missing?
If the price he sells at is $$\displaystyle (9+y), then he can expect to sell \displaystyle (30-3y) necklaces. So if he sells \displaystyle x necklaces \displaystyle x = 30 -3y \displaystyle \Rightarrow y = 10-\tfrac13x \displaystyle \Rightarrow he sells at$$\displaystyle (9+10-\tfrac13x)$= $$\displaystyle (19-\tfrac13x) So his profit is$$\displaystyle (19-\tfrac13x)x -8x$ = \displaystyle (11x -\tfrac13x^2)\$