University of Bahrain Course: ITIS331 Prepared By: Dr. Jihene Kaabi

Department of Information Systems Second Semester: 2014-2015

Solution is in page 2

Lab 3 Problem 1: Fashion factory produces five types of products (Shirt, Blouse, Dress, Jeans, and Jacket) by using two production processes: Cutting and Stitching. After deducting raw material costs each unit of product yields the following contributions to profit: Shirt

Blouse

Dress

Jeans

Jacket

$550

$600

$350

$400

$200

Each unit requires a certain time on each process. These are given below (in hours). A dash indicates when a process is not needed. Cutting Stitching

Shirt 12 10

Blouse 20 8

Dress 16

Jeans 25 -

Jacket 15 -

In addition the final assembly of each unit of each product uses 20 hours of an employee’s time. The factory has three Cutting machines and two Stitching machines and works a six-day week with two shifts of 8 hours on each day. Eight workers are employed in assembly, each working one shift a day. The problem is to find how much to make of each product so as to maximize the total profit contribution. 1. Develop a linear programming model for the above given problem. 2. Solve the developed model using Excel Solver. 3. Conduct a sensitivity analysis for the different model parameters.

University of Bahrain Course: ITIS331

Department of Information Systems First Semester: 2013-2014

Decision Variables: let Xi be number of Producti, i =1, i<=5 Objective Function: Zmax= 550X1 + 600X2 + 350X3 + 400X4 + 200X5 Constraints: Process 1 : Cutting 12X1 + 20X2 + 0X3 + 25X4 + 15X5 <= 289 (3 machines *6 days * 2 shift *8 hours) Process 2 : stiching 10X1 + 8X2 + 16X3 + 0X4 + 0X5 <= 192 (2 machines *6 days * 2 shift *8 hours) Employees Time 20(X1+ X2 + X3 + X4 + X5) <= 384 (8 workers * 6 days * 1 shift * 8hrs) 20X1+ 20X2 + 20X3 + 20X4 + 20X5 <= 384 Non-Negitivity Constraints: Xi >= 0; i=1, i<=6

Opimal Solution: to achieve the maximum profit (10920) the factory has to produce 12 units of product 1, 7 units of product 2, and zero units of Product 3,4 and5

Sensitivity analysis: Ci ? 550 - 50 <= C1 <= 550 + 50 500 <= C1 <= 600 600 - 50 <= C2 <= 600 + 83.33 550 <= C2 <= 683.33 C3 <= 350 + 125 C3 <= 475 C4 <= 400 + 231.25 C4 <= 631.26 C5 <= 200 + 368.75 C5 <= 568.75

University of Bahrain Course: ITIS331

Department of Information Systems First Semester: 2013-2014

bi ? 288 – 57.6 <= b1 <= 288 + 96 230.4 <= b1 <= 384 192 – 14.4 <= b2 177.6 <= b2 384 – 96 <= b3 <= 384 + 22.15 288 <= b3 <= 406.15

ai ? Constraint 1 is binding because its parameters are sensitive Constraint 2 is not binding because its parameters are not sensitive. Constraint 3 is binding because its parameters are sensitive.