Revenue Question with Linear Function HELP

[AnnaSuxCalc]

Revenue Question with Linear Function **HELP**

Homework Statement

(a) Express revenue (R=pq) as a function solely of p
(b) Sketch the graph of R as a function of p. Clearly label the x-intercept(s), y-intercept(s), and vertex (if there is one)
(c) At what price should you sell the Pen Tablets to get the largest revenue? What is the largest possible monthly revenue?

Homework Equations

q = -0.5p + 140 <-- demand function for Pen Tablets
q --> number of Pen Tablets that can be sold/month
p --> price ($) per Pen Tablet

The Attempt at a Solution

Once again I need a little help getting started on part (a), how can I make this be a function of only p

PLEASE HELP get my STARTED on this!

 

[Mark44]

a) If R = p*q and q = -0.5p + 140, can you rewrite R solely in terms of p?

 

[AnnaSuxCalc]

a) If R = p*q and q = -0.5p + 140, can you rewrite R solely in terms of p?

Mark:!) Yes I can lol:
R = p(-0.5p + 140)
R = -0.5p² + 140p

 

[Mark44]

Well, good!
What does the graph look like (part b)? Be sure to label the vertex, since that figures into part c.

 

[AnnaSuxCalc]

R = -0.5p² + 140p --> y = -0.5x² + 140x
Use the Quadratic Formula to find the two values of x:
x=-140 +/- $$\sqrt{140^2 - 4(-0.5)(0)}$$ /2(-0.5)
x = 280 OR 0

when x = 280
y = -0.5(280)² + 140(280)
y = -39200 + 39200
y = 0
when x = 0
y = -0.5(0)² + 140(0)
y = 0

--> therefore the two intercepts are (280,0) and (0,0)
Vertex:
h=-b/2a
h=-140/2(-0.5)
h=140

y=-0.5(140)² + 140(140)
y=9800

--> therefore the vertex is (140,9800)

now, for part (c)which one is which

 

[NoMoreExams]

Well how do you find the largest anything in calculus?

 

[AnnaSuxCalc]

Well how do you find the largest anything in calculus?

Uuhm...I have no Idea
dont I use the vertex to find this?
so --> the vertex is (140,9800)
is the 140 the p ? cos if it is I would sub p into the equation q = -0.5p + 140
so that q = -0.5(140) + 140
then q = 70
THEN
R = pq = 70*140 = 9800 ---> lol you I knew the R was the y part of the vertex...
anyways if NOT I just did a whole lot of typing for nothing

 

[Mark44]

Why did you change to x and y? Now you don't know which one is which. The variable p (unit price) and R (total revenue) would be more helpful to keep things straight.

And here's the question for c):
At what price should you sell the Pen Tablets to get the largest revenue? What is the largest possible monthly revenue?

 

[AnnaSuxCalc]

I know Mark lol...I have no Idea why I changed it..it seemed easier at the time
sooo the fact that your not responding to my calculation means that they are...wrong?!
I drew the graph and the y-axis is the R and the x-axis is the p
so to answer (c):
I should sell the Pen Tablets at $140 to get the largest revenue AND The largest possible monthly revenue is $9800!
Correct?!

 

[NoMoreExams]

Looks good.

 

[AnnaSuxCalc]

Woohoo!:!)