Question

QUESTION 13 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, o otherwise X2=1 if alternative 2 is selected, o otherwise X3=1 if alternative 3 is selected, o 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

Question 13:

The optimal Solution is X1 = 0, X2 = 1, X3 = 1

The Left-hand side of constraint for Budget is 25000*X1 + 32000*X2 + 29000*X3

Substituting the optimal solution in the above equation,

25000 * 0 + 32000 * 1 + 29000 * 1 = 61000

Answer: 61000

Question 14:

The objective function = 5000*X1 + 7000*X2 + 9000*X3

The value of optimal objective function is obtained by substituting the optimal solution in above equation

5000 * 0 + 7000 * 1 + 9000 * 1 = 16000

Answer: 16000

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