Question

Complete the following 3 problems and attach your work.

1. 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. Answer the following questions:

1. Define the decision variables.
2. Write down the objective function.
3. Write down the constraint that the demand of workers for 2pm-3pm is satisfied.

  

2. For the optimization problem below:

1. Neatly sketch the feasible region.
2. Plot one objective function line and indicate the direction of improvement.
3. Give the optimal solution and the corresponding objective function value.

Maximize Z=3x₁+4x₂

       ST:   4x₁+2x₂≤20

6x₁+6x₂≤30

2x₁+4x₂≤16

x₁,x₂≥0

   

3. For the linear programming problem in Question 2, answer the following questions regarding solving it with the simplex method.

1. Develop the augmented form for this problem.
2. Identify the slack variables, an initial basic feasible (BF) solution (including basic and nonbasic variables), and the value of the objection function. Finally, determine whether the current BF solution is optimal and explain why/why not.
3. Perform one iteration to proper form from Gaussian elimination complete with the minimum ratio test, identification of the entering and leaving basic variable, and resulting values of both the BF solution and the objective function.

Answer 1