3 of 7 PROBLEM 2 (20 POINTS HADA, a newly established software company by one of
ID: 362806 • Letter: 3
Question
3 of 7 PROBLEM 2 (20 POINTS HADA, a newly established software company by one of KFUPM graduates, is concerned with developing Arabic CD-ROM software applications that it sells to major computer hardware and software manufacturers. The company is currently evaluating the feasibility of developing six new application. Specific information concerning each of these applications is summarized in the following table roject rogrammers ecte Application Development Cost Required Net Profit 18 20 16 28 34 3, 600, 000 4, 000, 000 3, 000,000 4,400, 000 6,200,000 1,100,000 940,00 760,000 1,260,000 1, 800,000 HADA has staff of 60 programmers and has allocated SR 3.5 Million for development of new applications a) Formulate a BILP model for the case faced by HADA (10 points) b) Write the modification to the above formulation for the following situations: (2 points each) If it is anticipated that those interested in application 4 will also be interested in application 5, and vice versa Thus, f either application 4 or application 5 is developed, the other must also be developed The concepts of application 2 makes sense only if application 1 is included. Thus, application 2 will be developed only if application 1 is developed. Applications 3 and 6 have similar themes: thus, if application 3 is developed, application 6 will not be developed, and vice versa To ensure quality products, HADA does not wish to expand its product line too rapidly. Accordingly, it wishes to develop at most three of the potential application products at this timeExplanation / Answer
a) BILP model
Xi is a binary variable, such that Xi = 1, if application i is selected for development, where i=1,2,3,4,5,6
Objective: Maximize Z = Pi*Xi , where Pi is the project net profit on application i
Constraints:
6X1 + 18X2 + 20X3 + 16X4 + 28X5 + 34X6 <= 60 (total staff of 60 programmers)
0.4X1 + 1.1X2 + 0.94X3 + 0.76X4 + 1.26X5 + 1.8X6 <= 3.5 (total fund of 3.5 million)
Xi = binary
b) Modification of the model requires following additional constraints:
X4 - X5 = 0
X1 - X2 >= 0
X3 + X6 <= 1
X1 + X2 + X3 + X4 + X5 + X6 <= 3
Xi = binary
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