IE3033 OPERATIONS RESEARCH I – HOMEWORK I
Due Date: November 5
Notes:
1) Form a group of minimum 2 members and maximum 3 members until 22.10.2015. E-mail your names,surnames and numbers to: umut.izer@marmara.edu.tr
2) Develop LINGO model for only two of the following five problems including set and data sections. You can find the problems that each group should solve at: http://mimoza.marmara.edu.tr/~umut.izer
3) The LINGO model must import data and export results using @file / @text functions or @ole function.
4) Also conclude a range analysis for the right-hand-sides of the constraints and variables.
5) Write down the LP formulation and the LINGO model in a report using MS Word. You should also evaluate the results, reduced costs and ranges in your report. The report, LINGO model file and also its input/output files must be mailed to: umut.izer@marmara.edu.tr
PROBLEM 1

PROBLEM 2
PROBLEM 3

PROBLEM 4
The technical staff of a hospital wishes to develop a computerized menu planning system. To start with, a lunch menu is sought. The menu is divided into three major categories: vegetables, meat, and dessert. At least one equivalent serving of each category is desired. The cost per serving of some suggested items as well as their content of carbohydrates, vitamins, protein, and fats is summarized.
Carbohydrates Vitamins Protein Fats Cost in $/Serving
Vegetables
Peas
Green Beans
Okra
Corn
Macaroni
Rice
Meat
Chicken
Beef
Fish
Dessert
Orange
Apple
Pudding
Jello
1
1
3
1
1
5
2
3
2
4
1
1
1
3
2
6
0
0
1
1
8
6
2
3
5
5
1
0
6
0
0
1
3
5
1
1
1
2
1
0
0
1
0
0
1
1
2
2
1
0
0
0
0.63
0.28
0.42
0.15
0.12
0.1
0.12
0.13
0.09
0.1
0.07
0.7
1.2
Suppose that the minimal requirements of carbohydrates, vitamins, protein, and fats per meal are respectively 5, 10, 10, and 2.

PROBLEM 5
A production manager is planning the schedule of three products on four machines. Each product can be manufactured on each of the machines. The unit production costs (in $) are summarized
Machine
Product 1 2 3 4
1
2
3
4
3
12
4
7
10
5
5
8
7
6
11
The time (in hours) required to produce each unit product on each of the machines is summarized.
Machine
Product
1
2
3
1
0.3
0.2
0.8
2
0.25
0.3
0.6
3
0.2
0.2
0.6
4
0.2
0.25
0.5
Suppose that 4000, 5000, and 3000 units of the products are required, and that the available machine hours are 1500, 1200, 1500, and 2000 respectively.