17. Given the following binary programming problem with one constraint: a. <ART

Question

17. Given the following binary programming problem with one constraint:

a.   <ART FILE="11_18eq01.EPS" W="171.441pt" H="26.847pt" XS="100%" YS="100%"/>

Maximize profit = $8,000X1 + 5,000X2 + 12,000X3

                              + 14,000X4 + 5,000X5 + 6,000X6

                              + 9,000X7 + 10,000X8

subject to              $65,000X1 + 41,000X2 + 75,000X3

                              + 100,000X4 + 55,000X5

                               + 69,000X6 + 82,000X7

                              + 70,000X8

Explanation / Answer

Let us introduce a slack variable in our constraint so that

65,000X1 + 41,000X2 + 75,000X3 + 100,000X4 + 55,000X5 + 69,000X6 + 82,000X7 + 70,000X8 + s = 500,000

Now in matrix notation, this can be written as

Now making the coefficient if X1=1, we get

The second row gives the values of X1, X2, ... , X8 and max Z = 79261.54

8000 5000 12000 14000 5000 6000 9000 10000 0 0 65000 41000 75000 100000 55000 69000 82000 70000 1 500000

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