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Why is this linear problem a alternate optimal solution Min 3X+3Y 1X+2Y less than 16 1X+1Y...

Why is this linear problem a alternate optimal solution Min 3X+3Y 1X+2Y less than 16 1X+1Y less than 10 5X + 3Y less than 45 x,y, greater than 0

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Answer #1

This is an alternate optimal solution as it has got more than one optimal solution.

Here the given problem is:

Min

3X + 3Y

s.t.

1X + 2Y ≤ 16

1X + 1Y ≤ 10

5X + 3Y ≤ 45

     X , Y ≥ 0

When solving the problem graphically we will start with 1x+2y<=16. Here take y as 0 and so x is 16 and when x is taken as 0 y will be 8. Thus points for this line will be (16,0) and (0,8)

For the line 1x+1y<=10 the points will be (10,0) and (0,10)

Lastly for 5x+3y<=45 the points will be (9,0) and (0,15)

The graph for the same is shown below:

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