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Solve graphically for the optimal solution to the following linear program:

1.
MIN 16X1 + 12X2
s.t. 8X1 + 4X2 <_ 36
X1 + X2 <_ 7
3X1 + 12X2 >_ 24
X1 + 5X2 >_ 20
X1, X2 >_ 0

2.
MIN 18X1 + 12X2
s.t. 8X1 + 4X2 <_ 36
X1 + X2 <_ 7
3X1 + 12X2 >_ 24
X1 + 5X2 >_ 10
X1, X2 >_ 0

3.
MIN 3X1 + 6X2
s.t. 1X1 + 2X2 <_ 50
1X1 + 1X2 >_ 10
5X1 + 3X2 <_ 45
X1, X2 >_ 0

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Solution Summary

An optimal solution for linear programs is assessed.

Solution Preview

Solve graphically for the optimal solution to the following linear program:

1.
MIN 16X1 + 12X2
s.t. 8X1 + 4X2 ≤ 36
X1 + X2 ≤ 7
3X1 + 12X2 ≥ 24
X1 + 5X2 ≥ 20
X1, X2 ≥ 0
Solution:

First graph all the inequalities on one graph.

The purple line represents the constraint 8X1 + 4X2 ≤ 36

The red line represents the constraint X1 + X2 ≤ 7

The blue line represents the constraint 3X1 + 12X2 ≥ 24

The green line represents the constraint X1 + 5X2 ≥ 20

The shaded region represents the feasible region.

The corner points are ...

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