Reference no: EM132264168

Homework Problems:

Note: The networks for all problems given here involve no more than 14 nodes. If we arrange the decision variables in tabular form, the total number of entries will be no more than 196 1_ 14 : 142. Therefore, it should be possible to specify the entire table as changing variable cells even in the standard version of Solver.

Problem 1 - The Oconee County, South Carolina, superintendent of education is responsible for assigning students to the three high schools in his county. A certain number of students have to travel to and from school by bus, as several sectors of the county are beyond walking distance from a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. Of course, if a student happens to live in a certain sector and is assigned to the high school in that sector, there is no need to bus that student because he or she can walk to school. The three schools are located in sectors B, C, and E. The table at the top of the next page reflects the number of high-school-age students living in each sector and the distance, in miles, from each sector to each school. Assuming that each high school has a capacity of 1,100 students, set up and solve Oconee County's problem as a transportation model.

Problem 2 - The Southern Rail Company ships coal by rail from three coal mines to meet the demand requirements of four coal depots. The following table shows the distances from the mines to the various depots and the availabilities and requirements for coal. Determine the best shipment of coal cars to minimize the total miles traveled by the cars.

Problem 3 - The manager of the O'Brian Glass Company is planning the production of automobile windshields for the next four months. The demand for the next four months is projected to be as shown in the following table.

O'Brian can normally produce 100 windshields in a month. This is done during regular production hours at a cost of $100 per windshield. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices: (1) He can produce up to 50 more windshields per month in overtime but at a cost of $130 per windshield; (2) he can purchase a limited number of windshields from a friendly competitor for resale at a cost of $150 each (the maximum number of outside purchases over the four-month period is 450 windshields); or (3) he can fill the demand from his on-hand inventory. The inventory carrying cost is $10 per windshield per month. Back orders are not permitted. Inventory on hand at the beginning of month 1 is 40 windshields.

Set up and solve this "production smoothing" problem as a transportation model to minimize cost. Hint: Set the various production options (e.g., regular production, outside purchase, etc.) as supply nodes and the monthly demands as the demand nodes.

Problem 4 - Kelly Spaugh, course scheduler of a technical college's business department, needs to assign instructors to courses next semester. As a criterion for judging who should teach each course, Kelly reviews the student evaluations of teaching for the past two years. Because each of the four professors taught each of the four courses at one time or another during the two-year period, Kelly is able to determine a course rating for each instructor. These ratings are shown in the table at the bottom of this page.

Find the best assignment of professors to courses to maximize the overall teaching ratings.