The productivity of workers at a shoe factory (in pairs of shoes per hour) can be modeled using the function p(h) = -2/7h + 5, where h is the number of hours. If a worker must create at least 3 pairs of shoes per hour for the company to be profitable, how long should the worker's shift be?

  no more than 7 hours

Step-by-step explanation:

You want p(h) ≥ 3, so ...

  p(h) ≥ 3

  -2/7h +5 ≥ 3

  2 ≥ 2/7h . . . . . . add 2/7h -3

  7 ≥ h . . . . . . . . . multiply by 7/2

The worker's shift should be 7 hours or less.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this