Question: Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.
Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.
| a. | Maximize | Z = 4x1 + 3x2 |
| Subject to |
| Material | 6x1 + 4x2 | 48 | lb | |
| Labor | 4x1 + 8x2 | 80 | hour | |
| x1, x2 | 0 |
1. What are the optimal values of the decision variables and Z?
2. Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
multiple choice 1
None of the constraints have any slack. Both constraints are binding.
The first constraint has a slack of 10.
The second constraint has a slack of 15.
3. Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? multiple choice 2
None of the constraints have any surplus.
The first constraint has a surplus of 15.
The second constraint has a surplus of 20.
4. Are any constraints redundant? If yes, which one(s)? multiple choice 3
Yes, the first constraint is redundant.
Yes, the second constraint is redundant.
No, there are no redundant constraint.
| b. | Maximize | Z = 2x1 + 10x2 |
| Subject to |
| Durability | 10x1 + 4x2 | 40 | week | |
| Strength | 1x1 + 6x2 | 24 | psi | |
| Time | 1x1 + 2x2 | 14 | hour | |
| x1, x2 | 0 |
1. What are the optimal values of the decision variables and Z? (Round your answers to 2 decimal places.)
2. Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
multiple choice 4
None of the constraints have any slack.
The first constraint has a slack of 10.
The second constraint has a slack of 15.
3. Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? multiple choice 5
None of the constraints have any surplus.
The first constraint has a surplus of 20.
The second constraint has a surplus of 15.
4. Are any constraints redundant? If yes, which one(s)? multiple choice 6
Yes, the first constraint is redundant.
Yes, the second constraint is redundant.
No, there are no redundant constraint.
| c. | Maximize | Z = 6A + 3B (revenue) |
| Subject to |
| Material | 20A + 6B | 600 | lb | |
| Machinery | 25A + 20B | 1,000 | hour | |
| Labor | 20A + 30B | 1,200 | hour | |
| A , B | 0 |
1. What are the optimal values of the decision variables and Z?
2. Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have?
multiple choice 7
The third constraint has a slack of 120.
The second constraint has a slack of 60.
The first constraint has a slack of 80.
3. Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? multiple choice 8
None of the constraints have any surplus.
The second constraint has a surplus of 15.
The first constraint has a surplus of 20.
4. Are any constraints redundant? If yes, which one(s)? multiple choice 9
Yes, the first constraint is redundant.
Yes, the second constraint is redundant.
No, there are no redundant constraint.
Prev
Question 1 of 6 Total1 of 6
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
Study Help