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Solving a linear programming problem with a more complex feasible region is no different from solving one with only one constraint. Just slide the objective function until it first makes contact with the feasible region.
What combination of high-grade and low grade fertilizer should the farmer buy. Remember his constraints are now:
| spend no more than $60: | 12x + 4y | ≤ 60 |
| buy more than a total of 9 bags: | x + y | ≤ 9 |
| and | ||
| already committed to buy at least 2 high grade: | x | ≥ 2 |
Use the applet to find the new solution. How do the new constraints affect the solution?
Use the applet to solve the following linear programming problems. (As usual, assume non-negativity constraints for x and y.)
a) maximize 2x+y subject to:
| 5x | + | 4y | ≤ 24 |
| 5.5y | ≤ 15 | ||
| x | + | y | ≥ 2 |
b) maximize x+5y subject to:
| 5x | + | 4y | ≤ 24 |
| 3x | + | 5y | ≤ 35 |
| 0.5y | ≥ 1.5 |
c) maximize 13x+7y subject to:
| 10x | + | 7.5y | ≤ 68 |
| 0.5x | - | 0.5y | ≤ 2.5 |
| 1.5x | + | y | ≥ 2 |
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