The owner of the Consolidated Machine Shop has $10,000 available to purchase a l

Question

The owner of the Consolidated Machine Shop has $10,000 available to purchase a lathe, a press, a grinder, or some combination thereof. The following 0-1 integer linear programming model has been developed to determine which of the three machines (lathe, x1; press, x2; or grinder, x3) should be purchased in order to maximize annual profit: maximize Z 1,000x +700 subject to 8003 (profit, S) $5,000 6,0002 4,000x3 10,000 (cost, S) ?, x2, x3 = 0 or 1 What would be the constraint that either lathe or press (not both) should be purchased? 1) x1 x2s0 2) x1x2 s1 3) xi-x2 1 4) x1-x2-0

Explanation / Answer

Ans:

Option 3 is correct.

x1-x2<=1

As,

when x1=1,x2=0,then x1-x2=1-0=1

when x1=0,x2=1,then x1-x2=0-1=-1

when x1=1,x2=1,the x1-x2=1-1=0

So,in each situation x1-x2<=1

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