Finding vertex

[juliemariefort]

Okay, one last one tonight.

I'm confused about finding vertex.

Here's the problem:

A plastic bottle company has determined that when x bottles are produced and sold, the profit is given by P(x)= -.2x^2+5.28x+90.948. Where P(x) is in hundreds of dollars.

- How many bottles should be produced and sold to achieve maximum profit?
-What will the maximum profit be?

To find the vertex, x= -b/2a so x=-5.28/2(-.2) = 13.2 hundreds of bottles = 1320 bottles. So, 1320 bottles should be produced and sold to achieve maximum profit?

The Cost = C(13.2)= -.2(13.2)^2+5.28(13.2)+90.948 = 9.53 hundreds of dollars = 953 dollars will be the maximum profit?

I do not know if this is right, but I tried! Thank you in advance for your help.

 

[mmm4444bot]

… profit is given by P(x)= -.2x^2+5.28x+90.948. Where P(x) is in hundreds of dollars …

… To find the vertex, x= -b/2a so x=-5.28/2(-.2) = 13.2 hundreds of bottles = 1320 bottles … <<< Were you told that x represents hundreds of bottles ?

You did not state this in the given information.

If x represents hundreds of bottles, then your calculation is correct.

(It might very well be this way because 13 bottles is practically nothing in terms of mass production.)

… The Cost = C(13.2)= -.2(13.2)^2+5.28(13.2)+90.948 … <<< Is this a typographical error?

There is no cost function given in this exercise. You defined a function P(x), not C(x).

P(13.2) represents profit, not cost.

… 953 dollars will be the maxium profit? I get a different results for profit.

P(13.2) = 125.796

The profit is $12,579.60 .

Check your arithmetic.

Here's a couple of notes about notation.

Please use grouping symbols when typing fractions that contain products.

You typed b/2a. I understand what you mean, but this is not clear.

Typing -b/(2a) makes it clear that symbol a belongs in the denominator, versus (-b/2)a, which is actually (-ab)/2.

Same goes for x=-5.28/2(-.2).

Type x = -5.28/[(2)(-0.2)] instead.

Also, it's easier to read expressions when there are spaces around plus signs, minus signs, and equal signs.

P(x) = -0.2x^2 + 5.28x + 90.948 instead of P(x)=-.2x^2+5.28x+90.948

 

[juliemariefort]

Wow, thank you. Yes, I was told that x is in hundreds of bottles.

You're right. no cost function here, just profit function. I stink at math; I have no idea what I am talking about!

90.948 was the number given in the profit function.

When I re-calculated, I got the same $ amount for maximum profit.

Very astute of you! You made it very easy to understand. Thanks again.