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 $-0.02s^2+11s-100$.