Question

A company has decided to use 0-1 (binary) integer programming to help to make some investment decisions. There are three possible investment alternatives from which to choose, but if it is decided that a particular alternative is to be selected, the entire cost of that alternative will be incurred (i.e., it is impossible to build one-half of a factory). The integer programming model is as follows: Max 5000X1 +7000X2+9000X3 S.t. X1+X2+X3<=2 (only 2 may be chosen) 25000X1+32000X2+29000X3<=62000 (budget limit) 16X1+14X2+19X3<=36 (resource limitation) All variables =0,1 where X1=1 if alternative 1 is selected, 0 otherwise X2=1 if alternative 2 is selected, 0 otherwise X3=1 if alternative 3 is selected, 0 otherwise The optimal solution is X1=0, X2=1, X3=1 According to information above, if the optimal solution is used, how much of the budget would be spent? QUESTION 14 Refer to the previous investment decision problem 13. According to information above, what would be the optimal value of the objective function?

Answer 1

let 9000 x X₂} P. Man. $5000x, 7ooux, & Now As the As the conition given, Xit X2 et X₂ We have take two values can means (At most ) equal 1. -)) 62000 V 2900oXz Budget limit {B} 25000X t 32000* + Resourse limitation {R} 16x, & 14 Xz a 1982 36 Lets take some values xz - B=0 R : 6 ;x20;X3 29600 19 R X2=1 ;xz 7 61000 R 33 X Xa a ¿Y 3.0 a ) B 250m R x X2 ; x3 =1 B suo00 a35 ; X2:1 ;x2=0 57000 30 . X21iX 3 - 0 ow to to 32our 14 But P man provox, + 7000x2+ gooty} we Consider must take optimum value > lie, X. 20; X2+1 ; *3-1 Po man 500x, & foroxat gooox 3 60x3} I 16ooo { Budget would be spent 61000 (from eqo}