ARsate,is cshea ofdevrthese applications m Development cost application aquir R

Question

ARsate,is cshea ofdevrthese applications m Development cost application aquir R 400,000 1,100,000 940,000 1,260, 000 800.000 200. -ara,, of 60 programe rs and has allocated iR 3.5 Manon development of new applications for points b) Formulate a BILP model for the case taced b HADA.11 Mrite the modification to the above formulation tor tollowing aituations: (2 points each) it is anticipated that those interested in apeicasio i11 also be interested in application 5, and vice vesss rhus, if either application 4 or application 5 is developed, the other must also be developed The concepts of application 2 makes sense only it application 1 is included. Thus, application 2 wil1 be developed only if application 1 is developed. . Applications 3 and 6 have similar themes: thus, if application 3 is developed, application 6 wil1 not be developed, and vice versa. its product line too rapidly. Accordingly, it wishes to develop at most three of the potential application products at this time. .To ensure quality products, HADA does not wish to expand

Explanation / Answer

a) Decision variables: Let Xi be a binary variable such that if Xi = 1, then project i is selected for development, otherwise not.

Objective: Max 2X1 + 3.6X2 + 4X3 + 3X4 + 4.4X5 + 6.2X6

s.t.

6X1+18X2+20X3+16X4+28X5+34X6 <= 60

.4X1+1.1X2+.94X3+.76X4+1.26X5+1.8X6 <= 3.5

Xi = {0,1}

b) Additional constraints for the required modifications follow

i) X4 = X5, or, X4 - X5 = 0

ii) X1 >= X2 or, X1 - X2 >= 0

iii) X3 + X6 <= 1

iv) X1 + X2 + X3 + X4 + X5 + X6 <= 3

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