The daily production of a company is modeled by the function p = -w^2 + 75w - 1200. the daily production, p, is dependent on the number of workers (w) present. if the break-even point is when p=0, what are the least and greatest number of workers the company must have present each day in order to break even? 50 points! will give brainliest!

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

$9.41

step-by-step explanation: