Question

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?

Answer 1

Answer:

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.