UGANDA TECHNOLOGY AND MANAGEMENT UNIVERSITY
SCHOOL OF COMPUTING AND ENGINEERING
MT 111
Operations Research
Test 1
Time: 1 Hour
Attempt both Questions
Question 1:
A construction contractor employs a given force of skilled workers and has a limited set of
specialized Machinery. There a number of categories of skilled workers, as well as a number of
classes of specialized machinery. The contractor has a number of construction projects underway
and has committed the company to completion dates for each of them.
Certain activities are common to the various projects and require the same inputs of labor and
equipment. The activities occur on various dates throughout the time span from project start to
project completion. However, the contractor does not have enough labor and equipment to work
on these activities on the same day on all projects.
Hence, the contractor wants to schedule the specialized work forces and specialized equipment
on the projects so that ideally no labor or equipment shortages do exist, extra costs must be
incurred for temporary workers or for equipment. A predetermined payment has already been
received for each project. Now, the contractor wants to keep construction costs to its minimum.
(16 Marks)
Define:
i.
ii.
iii.
iv.
Decision variables;
Parameters;
The objective function in words
Constraints in words.
Question 2:
Joe’s Arts Ltd., manufactures two types of wooden toys: soldiers and trains. A soldier sells for
$27 and uses $10 worth of raw materials. Each soldier that is manufactured increases Joe’s Arts
variable labor and overhead costs by $14. A train sells for $21 and uses $9 worth of raw
materials. Each train built increases Joe’s Arts variable labor and overhead costs by $10. The
manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and
finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train
requires 1 hour of finishing and 1 hour of carpentry labor. Each week, Joe can obtain all the
needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for trains is
unlimited, but at most 40 soldiers are bought each week. Joe wants to maximize weekly profit
(revenues costs).
Formulate a mathematical model of Joe’s Arts situation that can be used to maximize Joe’s Arts
weekly profit. Solve the Model using Graphical Method. (24 Marks)