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
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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