Question

A manufacturer has recorded the profit P (in dollars) when there is a monthly advertising expenditure
of A dollars.

The data is recorded in the following table.
A 200 500 800 1100 1300
P 8030 14,480 14,630 8480 860

(a) Find a quadratic model for profit as a function of advertising expenditure.
(b) What advertising expenditure gives a maximum prot, and what is that profit?

Answer 1

I find it helpful to use Newton's divided difference:

8030 + 21.5(x-200) + (-0.035)(x-200)(x-500)
= 1/200 (-7x^2+9200x+46000)

further analysis at

http://www.wolframalpha.com/input/?i=8030+%2B+21.5%28x-200%29+%2B+%28-0.035%29%28x-200%29%28x-500%29