word problem modeling function

• Apr 24th 2007, 12:10 PM
keith
word problem modeling function
We are given the following information: The daily profits of a cigar company from selling x cigars are given by: p(x) = -.05x^2 + 100x - 2000
The government wishes to impose a tax on cigars (sometimes called a sin tax) That gives the company the option of either paying a flat tax of \$ 10,000 per day or a tax of 10% on profits. As chief financial officer of the company, one needs to decide which tax is the better option for the company.
a. Determine the profit function for each of the tax options.
Using the above equation I came up with these two:
(-.05x^2 + 100x -2000) - 1000 = -2005
(-.05x^2 + 100x -2000) - .10(-.05x^2+100x-2000) = -905
Am I on the right track with these?
Thank You,
Keith
• Apr 24th 2007, 01:43 PM
Jhevon
Quote:

Originally Posted by keith
We are given the following information: The daily profits of a cigar company from selling x cigars are given by: p(x) = -.05x^2 + 100x - 2000
The government wishes to impose a tax on cigars (sometimes called a sin tax) That gives the company the option of either paying a flat tax of \$ 10,000 per day or a tax of 10% on profits. As chief financial officer of the company, one needs to decide which tax is the better option for the company.
a. Determine the profit function for each of the tax options.
Using the above equation I came up with these two:
(-.05x^2 + 100x -2000) - 1000 = -2005
(-.05x^2 + 100x -2000) - .10(-.05x^2+100x-2000) = -905
Am I on the right track with these?
Thank You,
Keith

why did you equate the first to -2005 and the second to -905?

Let paying a flat tax of \$ 10,000 per day be tax option 1
Let a tax of 10% on profits be tax option 2

Then,

For option 1:
p(x) = -.05x^2 + 100x - 2000 - 10000

so p(x) = -.05x^2 + 100x - 12000 for option 1

For option 2:
p(x) = (-.05x^2 + 100x -2000) - .10(-.05x^2 + 100x - 2000)
= -.05x^2 + 100x -2000 + 0.005x^2 - 10x + 200
= -0.495x^2 + 90x - 1800

so p(x) = -0.495x^2 + 90x - 1800 for option 2