MGT3410 Management Linear Programming Model

MGT 3410 Management Linear Programming Model Questions

MGT 3410 Homework 4 Chapter 8&9 and 11

Summer 2023

1. Silver Star Bicycle Company will be manufacturing both men’s and women’s models of its Easy-Pedal bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men’s and 125 women’s models to be shipped during the first month and 200 men’s and 150 women’s models to be shipped during the second month. Additional data are shown:

Model Production Costs Current Inventory

Men’s    $120  20  

Women’s   90  30

The company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months.

Formulate this problem as a linear programming model so that a production schedule can be established in order to minimize production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements.

2. Adirondack Paper Mills, Inc., operates paper plants in Augusta, Maine, and Tupper Lake, New York. Warehouse facilities are located in Albany, New York, and Portsmouth, New Hampshire. Distributors are located in Boston, New York, and Philadelphia. The plant capacities and distributor demands for the next month are as follows:

Plant                   Capacity (units)  

Augusta               300

Tupper Lake        100

Distributor Capacity (units) Boston 150 New York 100 Philadelphia 150 The unit transportation costs (in $) for shipments from the two plants to the two warehouses and from the two warehouses to the three distributors are as follows: Warehouse Plant Albany Portsmouth Augusta 7 5 Tupper Lake 3 4 Warehouse Albany Portsmouth Boston 8 5 Distributor New York Philadelphia 5 7 6 10

a. Draw the network representation of the Adirondack Paper Mills problem.

b. Formulate the Adirondack Paper Mills problem as a linear programming problem. You do not need to solve the model.

3. Embassy Club Condominium, located on the west coast of Florida, is undertaking a summer renovation of its main building. The project is scheduled to begin May 1, and a September 1 (17-week) complete date is desired. The condominium manager identified the following renovation activities and their estimated times:

 Activity A B C D E F G H Immediate Predecessor ---A, B, C C, D A D, F E Time 3 1 2 4 5 3 6 4

a. Draw a project network.

b. What are the critical activities?

c. Will the project be completed by September 1?

4. Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company. Doug listed the following activity information for this project:

Activity Immediate Time (weeks) Predecessor Optimistic Most Probable A -1.5 2.0 B A 2.0 2.5 C -1.0 2.0 D C 1.5 2.0 E B, D 0.5 1.0 F E 1.0 2.0 G B, D 3.0 3.5 H G 3.0 4.0 I F, H 1.5 2.0 Pessimistic 2.5 6.0 3.0 2.5 1.5 3.0 7.0 5.0 2.5

a. Draw a project network.

b. What are the critical activities and what is the expected project completion time?

c. If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project?

Note: Homework solution must be submitted electronically to Homework 4 folder in Assignment on D2L.

It is your choice to submit all of your work or just the final answer only. If you only submit the final answer and the answer is wrong, you will lose all the points assigned to that question. If you also show the steps how you get that answer, you still can earn partial credit as long as the steps are not completely wrong.