Can someone help with these two word problems?

Question

These are giving me trouble. Can someone help me out?

1. The profits of a company are found by subtracting the company's cost from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by the 40x - 0.0002x^2, what is an expression for the profit?

2. A rectangle has an area given by A = x^2 + 5x + 6. Find expressions for the possible length and width of the rectangle.

Thanks!

Answer 1

1. Profit = revenue - cost
....= 40x - 0.0002x^2 - 14x - 120000
....= 26x - 0.0002x^2 - 14x - 120000

2. (x-3)(x-2)
....x = 3, 2

Answer 2

Profit = 40x-0.0002x^2-(14x +120,000)
Profit = 40x -0.0002x^2 -14x -120,000
Profit = 26x -0.0002x^2-120,000

A= x^2+5x +6 =(x+2)(x+3)
If x = 1, possible dimensions would be 3 X 4
If x = 2. possible dimensions would be 4 X 5
If x = 0 possible dimensions would be 3 X 2 or 6 X1.

Put in a value for x and get your answer. Make sure x the value you select does not make either factor 0 or negative.

Answer 3

1. (40x-0.0002x^2)-(14x+120,000)

-0.0002x^2+26x-120,000

Use the quadratic formula which is found in your book:

a=0.0002
b=-26
c=120,000

2. x^2+5x+6

Same process as above:

a=1
b=5
c=6