Question

The UMass IIE student chapter is going to run a fundraising event from 1pm through 5pm. Due to the large scale of the event, student workers will be hired to work for the event and each worker will be assigned to a particular shift. There are three shifts: 1pm-3pm, 2pm-4pm, 3pm-5pm. The pay for each of the three shifts is $20, $24 and $28 per worker respectively. The minimum number of workers needed for each hour is listed below: 1pm-2pm: 20, 2pm-3pm: 25, 3pm-4pm: 25, 4pm-5pm: 30. ASCE would like to minimize the hiring cost while satisfying the demand of workers in each hour.
A) Define the decision variables.
B) Write down the objective function.
C) Write down the constraint that the demand of workers for 2pm-3pm is satisfied.

Answer 1

Answer:

a. x1,x2,x3,x4

b. 20x1 + 24x2 + 28x3

c. x1 +x2 ≥ 25

Step-by-step explanation:

At a time that spans from 1 to 5pm, we have timing as follows:

1pm - 2pm = x1

2pm - 3pm = x2

3pm - 4pm = x3

4pm - 5pm = x4

a. The decision variables are x1, x2, x3, x4 and these are the number of people for each shift.

b. The objective function is the minimum cost which is

20x1 + 24x2 + 28x3

c. The constraints for each has been listed

1 - 2pm, x1 ≥ 20 workers

2 - 3pm, x1 + x2 ≥ 25

3 - 4pm, x2 + x3 ≥ 25

4 - 5pm, x3 ≥ 30

The question asked us to write the one for 2-3pm, which is x1 + x2 ≥ 25