Answer:
w= 52 and w = 23
Step-by-step explanation:
p = -w^2 + 75w - 1200
We want to solve at the break even point, when p=0
0 = -w^2 + 75w - 1200
Add 1200 to each side
1200 = -w^2 + 75w - 1200+1200
1200 = -w^2 + 75w
Factor out a minus sign from the right side
1200 = -(w^2 -75w)
Divide by -1
-1200 = w^2-75w
We will compete the square
-75/ 2 = -37.5 Then we square it (-37.5) ^2 =1406.25
Add 1406.25 to each side
1406.25 -1200 = w^2-75w +1406.25
206.25= (w-37.5)^2
Take the square root of each side
±sqrt(206.25) = sqrt( (w-37.5)^2)
±sqrt(206.25) = (w-37.5)
Add 37.5 to each side
37.5 ±sqrt(206.25) = (w-37.5)+37.5
37.5 ±sqrt(206.25) = w
There are two solutions
w =37.5 +sqrt(206.25) = 51.861
w =37.5 -sqrt(206.25) = 23.139
Rounding to the nearest worker
w= 52 and w = 23
