Problem 3 Transportation Problem

Apples are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload (in hundreds of dollars), supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago:

Formulate this problem as a linear programming model and solve it by using the computer.

Problem 4 Linear Programming

Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational boatsa fishing (bass) boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table:

The company has incurred fixed costs of $2,800,000 to set up its manufacturing operation and begin production. Lakeside has also entered into agreements with several boat dealers in the region to provide a minimum of 70 bass boats, 50 ski boats, and 50 speedboats. Alternatively, the company is unsure of what actual demand will be, so it has decided to limit production to no more than 120 of any one boat. The company wants to determine the number of boats that it must sell to break even while minimizing its total variable cost.

(a) Formulate a linear programming model for this problem.

(b) Solve the model by using the computer.

Problem 5 Project Management

During a violent thunderstorm with very high wind gusts in the third week of March, the broadcast tower for the public radio station WVPR, atop Poor Mountain in Roanoke, collapsed. This greatly reduced the strength of the stations signal in the area. The station management immediately began plans to construct a new tower. Following is a list of the required activities for building the new tower with optimistic (a), most likely (m), and pessimistic (b) time estimates (in days); however, the sequence of the activities has not been designated:

Using your best judgment, develop a CPM/PERT network for this project and determine the expected

project completion time. Also determine the probability that the station signal will be back at full strength within 3 months.

Boat Variable Cost Selling Price Bass Ski Speed $12,500 8,500 13,700 $23,000 18,000 26,000 Time Estimates (days) Activity Activity Description Removal of debris Survey new tower site Procure structural steel Procure electrical/broadcasting equipment Grade tower site Pour concrete footings and anchors Deliver and unload steel Deliver and unload electrical/broadcast equipment Erect tower Connect electrical cables between tower and building Construct storm drains and tiles Backfill and grade tower site Clean up Obtain inspection approval - wat was aware Boat Variable Cost Selling Price Bass Ski Speed $12,500 8,500 13,700 $23,000 18,000 26,000 Time Estimates (days) Activity Activity Description Removal of debris Survey new tower site Procure structural steel Procure electrical/broadcasting equipment Grade tower site Pour concrete footings and anchors Deliver and unload steel Deliver and unload electrical/broadcast equipment Erect tower Connect electrical cables between tower and building Construct storm drains and tiles Backfill and grade tower site Clean up Obtain inspection approval - wat was aware