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Math 174 - Mathematical Modeling: Camille Faye Euxine B. Tejano December 1, 2024

The document presents three mathematical optimization problems involving two variables, x1 and x2, with various constraints. The optimal solutions for each problem are provided along with the corresponding optimal values: 21 for the first, 144 for the second, and 280 for the third. Each problem confirms the feasibility of the solution based on the given constraints.

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5 views2 pages

Math 174 - Mathematical Modeling: Camille Faye Euxine B. Tejano December 1, 2024

The document presents three mathematical optimization problems involving two variables, x1 and x2, with various constraints. The optimal solutions for each problem are provided along with the corresponding optimal values: 21 for the first, 144 for the second, and 280 for the third. Each problem confirms the feasibility of the solution based on the given constraints.

Uploaded by

mowkieberse
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Math 174 — Mathematical Modeling

Camille Faye Euxine B. Tejano


December 1, 2024

1. optimize 2x1 + 3x2




 2x1 + 3x2 ≥ 6
3x1 − x2 ≤ 15



subject to −x1 + x2 ≤ 4

2x1 + 5x2 ≤ 27





x , x ≥ 0
1 2

2. optimize 6x1 + 4x2



 −x1 + x2 ≤ 12

x + x ≤ 24
1 2
subject to


 2x 1 + 5x 2 ≤ 80
x1 , x2 ≥ 0

3. optimize 10x
 1 + 35x2

 8x1 + 6x2 ≤ 48

4x + x ≤ 20
1 2
subject to


 x 2 ≥ 5
x1 , x2 ≥ 0

(Using Excel)
1.
The optimal solution is at x1 = 6 and x2 = 3, yielding an optimal value of 21. For the constraints, c1
meets the requirements, c2 exactly meets the requirement, in c3 the inequality is satisfied, and c4 meets
the bound at 27. Hence, it has a feasible region, and it leads to the objective function value of 21.

2.
The optimal solution is at x1 = 24 and x2 = 0, yielding an optimal value of 144. For the constraints, c1
satisfies the inequality, c2 has the exact value of 24 , and c3 also satisfies the inequality. Hence, it has a
feasible region.

1
3.
The optimal solution is at x1 = 0 and x2 = 8, yielding an optimal value of 280. All the constraints
satisfy the inequality hence, it has a feasible region.

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