3. Consider the following linear programming problem: Max 50x, +34x2 10x, +7£49
ID: 3046386 • Letter: 3
Question
3. Consider the following linear programming problem: Max 50x, +34x2 10x, +7£49 x+x, 25 ,x 20 st. Write the problem in standard form. Identify slack/surplus variables. (5 points) b. Identify the feasible region and find the optimal solution. (10 points) c. What are the values of the slack and surplus variables at the optimal solution? (5 points) 4. Consider the following linear programming problem Max 5x, +5x, st. x1 100 280 2x, +4x2 s 400 x,,x220 a. Identify the feasible region. (7 points) b. Find all the extreme points points) list the value of xi and x2 at each extreme point. (8 c. What is the optimal solution? (5 points)Explanation / Answer
3)
Tableau #1
x1 x2 s1 s2 p
10 7 1 0 0 49
1 1 0 -1 0 5
-50 -34 0 0 1 0
Tableau #2
x1 x2 s1 s2 p
1 0.7 0.1 0 0 4.9
0 0.3 -0.1 -1 0 0.1
0 1 5 0 1 245
Tableau #3
x1 x2 s1 s2 p
1 0 0.333333 2.33333 0 4.66667
0 1 -0.333333 -3.33333 0 0.333333
0 0 5.33333 3.33333 1 244.667
Optimal Solution: p = 244.667; x1 = 4.66667, x2 = 0.333333
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