A company's profits are given by f(t) = -t^2 + 7t - 2

[wilc0919]

The following is the question and my answers. I would appreciate knowing if my answers are right.

Question: A company's profits (in millions of dollars per year) as a function of time (in years) are given by the formula f(t) = -t^2 + 7t - 2, with t = 0 in 1980.

a) What is maximum profit the company earns?

I ANSWERED 10 MILLION DOLLARS

b) When does this maximum occur?

I PUT 1983 and 1984

Am I right? Thank you!

 

[james cook]

i find it to be 10.25 million and as it is a quadratic it has only one max at t =3.5 which is half way through 1983

 

[wilc0919]

Calculator

When I put the equation into the scientific calc. I get 10 TWICE for the Y value (dollars) in both 1983 and 1984...

THIS ISN'T RIGHT????????????

Are you SURE of your answer?????

 

[stapel]

When I put the equation into the scientific calc. I get 10 TWICE for the Y value (dollars) in both 1983 and 1984.

What do you mean by "putting the equation into a scientific calculator"...? Did your class not cover how to find the vertex of a parabola?

Thank you.

Eliz.

 

[wilc0919]

??

Yes, they did...but I am confused....
I am returning to this level math after a 20 year absence....

so what do I do?

 

[stapel]

Yes, they did...so what do I do?

Find the vertex (which is of course the maximal point) by whatever method they taught you.

Are you doing completing the square? Or using the formula? Are you needing links to lessons on the topic, so you can refresh?

Thank you.

Eliz.

 

[wilc0919]

I don't know HOW to do it

I don't know what to do????

We definitely haven't done completing the square....but how do I find the vertex?
ANd once I get THAT what does it tell me????????

 

[galactus]

Try graphing your function. You can easily see the max.

The vertex can be found by using $\displaystyle t=\frac{-b}{2a}$

That is the vertex, therefore, a max or min.

In your case it occurs at (7/2, 41/4). Since 1980 is 0, then 7/2 added to

that is 1983 and 6 months. When you plug 7/2 back into your function

you get 41/4 or 10.25. That's the max profit.

The max profit occurs halfway into 1983 with profit of 10.25 million dollars.

Just as James stated.

 

[wilc0919]

THANKS SOOOO MUCH

I actually spent 3 hours last night on it, and FINALLY got it on my own!!!!

I appreciate the help so much....your detailed explanation helped me check my work and now if I get another problem like that I WILL KNWO how to do it!!

YOOOO HOOOOOOOO!!!!!!!!