Question

In: Advanced Math

Consider the following all-integer linear program: Max 5x1 +8x2 s.t.   6x1 + 5x2 <= 30 9x1...

Consider the following all-integer linear program:

Max 5x1 +8x2

s.t.  

6x1 + 5x2 <= 30

9x1 + 4x2 <= 36

1x1 + 2x2 <=10

x1, x2 $ 0 and integer

a. Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.

b. Find the optimal solution to the LP Relaxation. Round down to find a feasible integer solution.

c. Find the optimal integer solution. Is it the same as the solution obtained in part (b) by rounding down?

I NEED EXCEL FILE THAT HAS EXCEL SPREAD SHEET AND SENSITIVITY REPORT TO SOLVE THIS PROBLEM (ALSO NEED STEP TO CREATE THEM)

Solutions

Expert Solution

spread sheet

MS EXCEL SHEET


Related Solutions

Consider the following all-integer linear program: Max x1 + x2 s.t. 4x1 + 6x2 ≤ 22...
Consider the following all-integer linear program: Max x1 + x2 s.t. 4x1 + 6x2 ≤ 22 x1 + 5x2 ≤ 15 2x1 + x2 ≤ 9   x1, x2 ≥ 0 and integer Solve the LP Relaxation of this problem. The optimal solution to the LP Relaxation is x1 = ___, x2 = .____________ Its value is ___________ Find the optimal integer solution. The optimal solution to the LP Relaxation is x1 = _____x2 = __________ Its value is _______
3. Consider the following all-integer linear program: Max 1x1+1x2 s.t. 4x1+6x2 ?22 1x1+5x2 ?15 2x1+1x2 ?9...
3. Consider the following all-integer linear program: Max 1x1+1x2 s.t. 4x1+6x2 ?22 1x1+5x2 ?15 2x1+1x2 ?9 x1, x2 ?0 and integer a. Graph the constraints for this problem. Use dots to indicate all feasible integer solutions. b. Solve the LP Relaxation of this problem. c. Find the optimal integer solution.
Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 –...
Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 – x1+ x2≤2 x2≤2.5 x1≥0, x2≥0 a. Show the equality form of the model. b. Sketch the graph of the feasible region and identify the extreme point solutions. From this representation find the optimal solution. c. Analytically determine all solutions that derive from the intersection of two constraints or nonnegativity restrictions. Identify whether or not these solutions are feasible, and indicate the corresponding objective function...
Consider the following linear program:    MAX Z = 25A + 30B    s.t. 12A +...
Consider the following linear program:    MAX Z = 25A + 30B    s.t. 12A + 15B ≤ 300    8A + 7B ≤ 168 10A + 14B ≤ 280    Solve this linear program graphically and determine the optimal quantities of A, B, and the    value of Z. Show the optimal area.
3. Consider the following linear program: MIN 6x1 + 9x2 ($ cost) s.t. x1 +2x2 ≤8...
3. Consider the following linear program: MIN 6x1 + 9x2 ($ cost) s.t. x1 +2x2 ≤8 10x1 + 7.5x2 ≥ 30 x2 ≥ 2 x1,x2 ≥0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 Variable Value Reduced Cost X1 1.500 0.000 X2 2.000 0.000 Constraint Slack/Surplus Dual Price 1 2.500 0.000 2 0.000 −0.600 3 0.000 −4.500 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 0.000 6.000 12.000 X2 4.500...
Consider the following linear program:    MAX Z = 25A + 30B    s.t. 12A + 15B ≤...
Consider the following linear program:    MAX Z = 25A + 30B    s.t. 12A + 15B ≤ 300    8A + 7B ≤ 168   10A + 14B ≤ 280    Solve this linear program graphically and determine the optimal quantities of A, B, and the    value of Z. Show the optimal area.
Consider the following linear program: Max 4A + 6B s.t. 9A + 3B ≥ 20 3A...
Consider the following linear program: Max 4A + 6B s.t. 9A + 3B ≥ 20 3A + 5B ≤ 15 2A ≤ 6 A, B ≥ 0
Simplex Method Consider the following linear programming problem: max z = 6x1 + 3x2 - 9x2...
Simplex Method Consider the following linear programming problem: max z = 6x1 + 3x2 - 9x2 - 9x3 + 15x4 s.t. 2x1 + 4x2 +6x3 + 8x4 <= 80    6x1 - 3x2 +3x3 + 6x4 <= 24    12x1 - 6x2 + 3x3 - 3x4 <= 30    x1, x2, x3, x4 >= 0 Rewrite the problem in standard form, that is, add the necessary slack variables in order to consider only equality constraints (and non-negativity). What is the...
Solve the following linear program using the graphical solution procedure. Max 5A + 5B s.t 1A...
Solve the following linear program using the graphical solution procedure. Max 5A + 5B s.t 1A <100 1B<80 2A+4B<400 A,B>0
2. Solve the following linear program using the graphical solution procedure: Max 8A + 5B s.t....
2. Solve the following linear program using the graphical solution procedure: Max 8A + 5B s.t. i. 1A ≤ 120 ii. 1B ≤ 150 iii. 2A + 4B ≤ 700 iv. A, B ≥ 0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT