Question

The profits of two different clothing factories can be modeled as shown, where s is the number of shirts produced at each factory.

Factory A: -0.06s²+43s-1600
Factory B: -0.04x²+32x-1500
a. Write a polynomial that represents the difference in the profits at the two plants.
b. Write a polynomial that represents the total profits from both plants.

Answer 1

To find the difference in profits, subtract Factory B's profit function from Factory A's, resulting in -0.02s² + 11s - 100. To find the total profits, add the profit functions of both factories, yielding -0.10s² + 75s - 3100.

Step-by-step explanation:

The correct answer is option to create a polynomial representing the difference in profits between the two factories, we subtract the profit function of Factory B from Factory A:

Factory A: -0.06s² + 43s - 1600

Factory B: -0.04s² + 32s - 1500

Difference in profits = Factory A - Factory B

= (-0.06s² + 43s - 1600) - (-0.04s² + 32s - 1500)

= (-0.06s² + 43s - 1600 + 0.04s² - 32s + 1500)

= -0.02s² + 11s - 100

To represent the total profits from both plants, we add the profit functions of Factory A and Factory B:

Total profits = Factory A + Factory B

= (-0.06s² + 43s - 1600) + (-0.04s² + 32s - 1500)

= (-0.06s² + 43s - 1600 - 0.04s² - 32s + 1500)

= -0.10s² + 75s - 3100.