A factory has received an order for a product. It takes 9 operations to manufacture it. These may take place in any order and at any time in the manufacturing process but an individual worker stays with one operation from its beginning to its end. The number of hours for one worker to complete each operation is as follows:

All workers are able to complete all operations, but can only do one at a time. The product has to be ready in 16 hours.

What is the minimum number of workers required to manufacture the product in the given time?

Determine what they are trying to ask, and what you will need to solve it

Eliminate any non-essential information

Draw a picture, graph, or equation

In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.

Solve.

Approach: Examine the numbers given. We will then add as many numbers as it takes to reach 16 or as close to 16 as possible. We are doing this to find out which workers can do more than one job in the allotted time, this way we are finding the minimum number of workers because we are wasting the least amount of hours possible.

Step A and H 12 hours + 4 hours = 16 hours

Step E and G 10 hours + 6 hours = 16 hours

Step B, F and I 3 hours + 2 hours + 10 hours = 15 hours

Keep track of the steps you have completed. You can cross them off with a pen on the exam paper.

We have C and D left, but they cannot be completed together.

Step C = 8 hours.

Step D = 9 hours.

There is no other rearrangement here that could give us any less workers.

\fcolorbox{red}{grey!30}{Therefore E is the answer because the minimum number of workers we need is $5$.}