A laundry owner's estimate of her weekly profits, is given by the equation p=-4w2+160w, where w represent the number of workers she hires. What is the number of workers she should hire in order to earn the greatest profit?

Number of workers = 20.

Step-by-step explanation:

p = - 4w^2 + 160 w

We need to find the value of w when p is a maximum.

We need to convert the equation to vertex form:

p = - 4w^2 + 160w

p = - 4 (x^2 - 40w)

p = - 4 [ (x - 20) ^2 - 400]

p = - 4 (x - 20) ^2 + 1600.

So the vertex is at (20, 1600)

The maximum profit is 1600 and the number of workers = 20.