Expert: Scotto - 1/20/2009

Question
This question is a 3 part question and i am having difficulties with the third part. The question reads as;
You are the marketing President of a Pen Tablet Company and you forecast that the demand equation for your Tablets is given by q= -0.5p +140 , where q is the number of Tablets your company can sell in a month if the price is p per Tablet.
a) Express revenue R (R=pq) as a function of p ;
my answer was p = (x-140)/(-0.5)

b) Sketch the graph and find the y and x intercepts;
my answer was a downwards slope with x intercept = 140  and y intercept = 280.

c) At what price should you sell the Tablets to get the largest revenue? What is the largest possible monthly revenue?;
This is where I am confused, it seems that is I was to do it like any other revenue problem I am missing some information. provided my answers are correct, do I use the intercepts in the beginning equation or is that not right?

Thank you

Answer
A was not done correctly, so the rest is not possible.  I'll do (a) and take it from there.

a) The answer is stated to be pq.  Since q = -0.5p +140 and the price is p, so the Revenue R = pq = p(-0.5p + 140).
Multiplying out this equation gives
R = -0.5p² + 140p.

b) A p can be factored out, so the equation is -p(0.5p - 140).
This means the zeros of the graph are where each term is 0.
That would be at p = 0 or 0.5p = 140 => p = 280.

c) Since it is a parabola, the maximum would be half way between the zeros of 0 and 280.  That is, (0+280)/2 = 140.