## A blending type linear programming problem:Use dual variables to model the problem 2. Examines how resources should be mixed in order to produce substances with specified characteristics

## linear programming problem

1. A blending type linear programming problem

1. | Uses dual variables to model the problem | |

2. | Examines how resources should be mixed in order to produce substances with specified characteristics | |

3. | Requires a blend of linear and non linear programming characteristics | |

4. | All of the above is true |

5 points

**Question 2**

1. Refer to Figure 17 on page 255 of your text book (Lindo Output for HAL). Assume the constraint functions represent resources. How many of the constraint resources have been completely used or exhausted?

1. | 1 | |

2. | 2 | |

3. | 3 | |

4. | 4 | |

5. | 5 |

5 points

**Question 3**

1. In a portfolio problem, X1, X2 and X3 represent the number of shares purchased of stocks 1, 2 and 3 which have selling price of $15, $47.25 and $109 respectively. If the investor has up to $50,000 to invest. An appropriate part of the linear programming model would be:

1. | 15X1 + 47.5X2 + 109X3 <= 50,000 | |

2. | Max 15X1 + 47.5X2 + 109X3 | |

3. | X1 + X2 + X3 <=50,000 | |

4. | Max ( 15X1) + 50(47.25X2) +50(109X3) |

5 points

**Question 4**

1. Read problem 2 on page 254 of your test. Read only the problem and exclude reading of the questions a through c. Also refer to the lindo output solution (page 255, figure 18, Output for Vivan s Gem ). How many diamonds have been used to formulate the optimum solution

1. | 30 | |

2. | 50 | |

3. | 11 | |

4. | None of the above |

5 points

**Question 5**

1. Read problem 2 on page 254 of your test. Read only the problem and exclude reading of the questions a through c. Also refer to the lindo output solution (page 255, figure 18, Output for Vivan s Gem ). Which of the following statements is true?

1. | No type two rings were produced | |

2. | 30 rubies were used to formulate the optimum solution | |

3. | 50 Type 1 rings were produced | |

4. | 11 diamonds were used to formulate the optimum solution | |

5. | none of the above |

5 points

**Question 6**

1. Read problem 2 on page 254 of your test. Read only the problem and exclude reading of the questions a through c. Also refer to the lindo output solution (page 255, figure 18, Output for Vivan s Gem ). How many rubies have been used to formulate the optimum solution

1. | 30 | |

2. | 50 | |

3. | 11 | |

4. | None of the above |

5 points

**Question 7**

1. When an artificial variable remains in the final tableau

1. | The problem is infeasible | |

2. | The problem is unbound | |

3. | The problem is optimal | |

4. | The problem has multiple optimal solutions | |

5. | The problem is degenerate |

5 points

**Question 8**

1. When there is a tie in ratio test for the determination of the exiting variable,

1. | The problem is infeasible | |

2. | The problem is unbound | |

3. | The problem is optimal | |

4. | The problem has multiple optimal solutions | |

5. | The problem is degenerate |

5 points

**Question 9**

1. A solution is unbound when

1. | There is a tie in the ratio test for the determination of the exiting variable | |

2. | An exiting variable cannot be determined | |

3. | An artificial variable remains in the optimal tableau | |

4. | A non basic variable has a value of zero in the objective function row within the tableau | |

5. | None of the above |

5 points

**Question 10**

1. A minimization problem with four decision variables, two greater than or equal to constraints, and one equality constraint will have

1. | 2 surplus variables, 3 artificial variables and 3 variables in the basis | |

2. | 4 surplus variables, 2 artificial variables and 4 variables in the basis | |

3. | 3 surplus variables, 3 artificial variables and 4 variables in the basis | |

4. | 2 surplus variables, 2 artificial variables, and 3 variables in the basis |

5 points

**Question 11**

1. ____________ solutions are ones that satisfy all of the constraints simultaneously

1. | alternate / multiple optimal | |

2. | feasible | |

3. | deviate | |

4. | optimal |

5 points

**Question 12**

1. Multiple optimal solutions exist when,

1. | There is a tie in the ratio test for the determination of the exiting variable | |

2. | An exiting variable cannot be determined | |

3. | An artificial variable remains in the optimal tableau | |

4. | A non basic variable has a value of zero in the objective function row within the tableau | |

5. | None of the above |

5 points

**Question 13**

1. Refer to Figure 17 on page 255 of your text book (Lindo Output for HAL). Which of the following statements is true

1. | Three of the slack variables are basic, the remaining three are nonbasic | |

2. | All of the real decision variables are basic | |

3. | There are a total of nine basic and nonbasic variables | |

4. | All of the above is true | |

5. | None of the above is true |

5 points

**Question 14**

1. Read problem 1 on page 254 of your text. Read only the problem and exclude reading of the questions a through d. Also refer to the lindo output solution (page 255, figure 17). How much labor has been used to produce the computers?

1. | 800 | |

2. | 1000 | |

3. | 4000 | |

4. | None of the above |

5 points

**Question 15**

1. Read problem 1 on page 254 of your text. Read only the problem and exclude reading of the questions a through d. Also refer to the lindo output solution (page 255, figure 17). How many computers (total) have been produced in Los Angeles

1. | 800 | |

2. | 1000 | |

3. | 4000 | |

4. | None of the above |

5 points

**Question 16**

1. All basic feasible solutions from n variables and m constraints, where n is greater than m (N > M)

1. | Have no negative values for any of the variables | |

2. | Have non basic variables in the amount of n-m | |

3. | Have m amount of basic variables | |

4. | All of the above | |

5. | None of the above |

5 points

**Question 17**

1. In a portfolio problem, X1, X2 and X3 represent the number of shares purchased of stocks 1, 2 and 3 which have selling price of $15, $47.25 and $109 respectively. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is appropriate?

1. | X1 <= .35 | |

2. | X1 <= .35(5000) | |

3. | X1 <= .35(X1 + X2 + X3) | |

4. | X1 <= .35(X1 + X3) |

5 points

**Question 18**

1. In a portfolio problem, X1, X2 and X3 represent the number of shares purchased of stocks 1, 2 and 3 which have selling price of $15, $47.25 and $109 respectively. The stockbroker suggest limiting the investment so that no more than $10,000 is invested in stock 2 or the total number of shares purchased of stocks 2 and 3 does not exceed 350, which ever is more restrictive. How would this be specified in a constraint?

1. | 10000 X2 <= 350 X2 + 350 X3 | |

2. | X2 <= 10000 & X2 + X3 <= 350 | |

3. | 47.25X2 <= 10000 & X2 + X3 <= 350 | |

4. | 47.25 X2 <= 10000 & 47.25 X2 + 109 X3 <= 350 |

5 points

**Question 19**

1. Given three variables: X1, X2 and X3 representing production of three products, a constraint representing the amount of product 1 from being no more than one half the total production of all three products would be written as

1. | 2X1 + X2 + X3 >= 0 | |

2. | ½ X1+ X2 + X3 <= 0 | |

3. | X1 + ½ X2- ½- X3 <=0 | |

4. | ½ X1 – ½ X2 – ½ X3 <=0 |

5 points

**Question 20**

1. Given two variables X1 and X2 which represent quantities to be blended, a constraint requiring the ratio of substance 1 to substance 2 to be at least 40% would be written as

1. | X1 – .4X2 >= 0 | |

2. | .4X1 X2 >= 0 | |

3. | X1 + X2 >= .4 | |

4. | X1 >=.4X2 |