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.

Answer 1

Note: It should be s instead of x in profit of factory B.

Given:

Consider 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 :
`-0.06s^2+43s-1600`

Factory B :
`-0.04s^2+32s-1500`

To find:

The polynomial that represents the difference in the profits at the two plants.

Solution:

Let,

Factory A :
`P_1=-0.06s^2+43s-1600`

Factory B :
`P_2=-0.04s^2+32s-1500`

Difference in the profits at the two plants is

`Difference= P_1-P_2`

`Difference= -0.06s^2+43s-1600-(-0.04s^2+32s-1500)`

`Difference= -0.06s^2+43s-1600+0.04s^2-32s+1500`

`Difference= (-0.06s^2+0.04s^2)+(43s-32s)+(-1600+1500)`

`Difference= -0.02s^2+11s-100`

Therefore, the required expression is
`-0.02s^2+11s-100`.