MGT3410 Optimal Solution – Consider the following linear programming

MGT 3410 Optimal Solution Questions

MGT 3410 Final Examination

Answer all questions (take-home examination)

Summer 2023

Academic Honesty Policy: I understand that this is an open books/notes exam and I may use a computer to perform computations as necessary. I have neither given nor received help on this exam.

Submit your solution electronically in a folder called “Final Examination” under Dropbox on D2L.

1. Consider the following linear programming problem:

Min s.t. 3???? + 4???? ???? + 3???? ≥ 6 ????+???? ≤4 ????, ???? ≥ 0

a. Write the problem in standard form. Identify slack/surplus variables. (5 points)

b. Find all the extreme points. You must list the value for x and y at each extreme point. (5 points)

 c. Find the optimal solution. (5 points) d. What are the values of the slack and surplus variables at the optimal solution? (4 points)

2. Thomas Industries and Washburn Corporation supply three firms (Zrox, Hewes, Rockwright) with customized shelving for its offices. They both order shelving from the same two manufacturers, Arnold Manufacturers and Supershelf, Inc. Because of long standing contracts based on past orders, unit costs from the manufacturers to the suppliers are given below:

Thomas 5 7 Arnold Supershelf Washburn 8 4 The chart below gives the cost to install the shelving at the various locations: Thomas Washburn Zrox 1 3 Hewes 5 4 Rockwright 8 4 Currently weekly demand by the user are 50 for Zorx, 60 for Hewes, and 40 for Rockwright. Both Arnold and Supershelf can supply at most 75 units to its customers.

a. Draw a network representation for this problem. (5 points)

b. Formulate this problem as a LP model. You don’t need to solve the model. (10 points)

3. Bart’s Barometer Business (BBB) is a retail outlet that deals exclusively with weather equipment. Currently BBB is trying to decide on an inventory and reorder policy for home barometers. These cost BBB $50 each and demand is about 500 per year distributed fairly evenly throughout the year. Reordering costs are $80 per order and holding costs are figured at 20% of the cost of the item. BBB is open 300 days a year (6 days a week and closed two weeks in August). Lead time is 60 working days.

a. Develop a total cost model for BBB. (4 point)

b. What is the optimal reorder quantity? (5 points)

c. What is the cycle time? (5 points)

d. What is the reorder policy for BBB? (5 points)

e. What total annual cost does the model give? (5 points)

 4. Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars): Service Full Price Discount Demand for Service Strong Weak $900 -$470 $650 $290

a. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the pessimistic and minimax regret approaches? (6 points)

b. Suppose that the management of Myrtle Air Express believes that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What are the expected value for each service? What is your recommended service based on the expected value approach? (6 points)

c. What is the EVPI given the information in part (b)? (5 points)

5. Given the following network with activities and times estimated in days, D A Start E B F C G H I J K Finish Activity Optimistic Most Probable Pessimistic A B C D E F G H I J K 3 1 4 8 3 6 4 3 5 12 1 5 3 7 11 4 9 6 6 7 13 3 7 5 10 14 5 12 8 9 15 14 5

a. Fill in all the blanks in the following table. (10 points) Note: For variance (σ2) in activity time, keep two decimal places. Activity Precedence Activities Expected Time t (days) Varianc e σ2 ES EF LS LF Slack Critical Path? A B C D E F G H I J K

b. What is the expected time and variance to complete the project? (5 points)

c. What is the probability the project will take more than 28 days to complete? (5 points)

d. If activity F is delayed by 6 days, how long will the project be delayed? (5 points)