Q6
1. Decision variables
a. tell how much or how many of something to produce, invest, purchase,
hire, etc.
b. represent the values of the constraints.
c. measure the objective function.
d. must exist for each constraint.
2. Which of the following is a valid objective function for a linear
programming problem?
a. Max 5xy
b. Min 4x + 3y + (2/3)z
c. Max 5x2 + 6y2
d. Min (x1 + x2)/x3
3. Which of the following statements is NOT true?
a. A feasible solution satisfies all constraints.
b. An optimal solution satisfies all constraints.
c. An infeasible solution violates all constraints.
d. A feasible solution point does not have to lie on the boundary of the
feasible region.
4. To find the optimal solution to a linear programming problem using
the graphical method
a. find the feasible point that is the farthest away from the origin.
b. find the feasible point that is at the highest location.
c. find the feasible point that is closest to the origin.
d. None of the alternatives is correct.
5. The improvement in the value of the objective function per unit
increase in a right-hand side is the
a. sensitivity value.
b. dual price.
c. constraint coefficient.
d. slack value.
6. Infeasibility means that the number of solutions to the linear
programming models that satisfies all constraints is
a. at least 1.
b. 0.
c. an infinite number.
d. at least 2.
7. A constraint that does not affect the feasible region is a
a. non-negativity constraint.
b. redundant constraint.
c. standard constraint.
d. slack constraint.
8. All linear programming problems have all of the following properties
EXCEPT
a. a linear objective function that is to be maximized or minimized.
b. a set of linear constraints.
c. alternative optimal solutions.
d. variables that are all restricted to nonnegative values.
part b – problems (30 points each)
Q6
1. Consider the following linear programming problem
Max 8X + 7Y
s.t. 15X + 5Y < 75
10X + 6Y < 60
X + Y < 8
X, Y ( 0
a. Set up and solve using Lindo.
b. What are the values of X and Y at the optimal solution?
c. What is the optimal value of the objective function?
Max 20X + 10Y
s.t. 12X + 15Y < 180
15X + 10Y < 150
3X - 8Y < 0
X , Y > 0
a. Which area (I, II, III, IV, or V) forms the feasible region?
b. Which point (A, B, C, D, or E) is optimal?
c. Which constraints are binding?
d. Which slack variables are zero?
Mathematics Homework Solutions
#116923
Math for decision making
1. Decision variables
a. tell how much or how many of something to produce, invest, purchase, hire, etc.
b. represent the values of the constraints.
c. measure the objective function.
d. must exist for each constraint.
2. Which of the following is a valid objective function for a linear programming problem?
a. Max 5xy
b. Min 4x + 3y + (2/3)z
c. Max 5x2 + 6y2
d. Min (x1 + x2)/x3
3. Which of the following statements is NOT true?
a. A feasible solution satisfies all constraints.
b. An optimal solution satisfies all constraints.
c. An infeasible solution violates all constraints.
d. A feasible solution point does not have to lie on the boundary of the feasible region.
4. To find the optimal solution to a linear programming problem using the graphical method
a. find the feasible point that is the farthest away from the origin.
b. find the feasible point that is at the highest location.
c. find the feasible point that is closest to the origin.
d. None of the alternatives is correct.
5. The improvement in the value of the objective function per unit increase in a right-hand side is the
a. sensitivity value.
b. dual price.
c. constraint coefficient.
d. slack value.
6. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is
a. at least 1.
b. 0.
c. an infinite number.
d. at least 2.
7. A constraint that does not affect the feasible region is a
a. non-negativity constraint.
b. redundant constraint.
c. standard constraint.
d. slack constraint.
8. All linear programming problems have all of the following properties EXCEPT
a. a linear objective function that is to be maximized or minimized.
b. a set of linear constraints.
c. alternative optimal solutions.
d. variables that are all restricted to nonnegative values.
PART B ¡V PROBLEMS (30 POINTS EACH)
1. Consider the following linear programming problem
Max 8X + 7Y
s.t. 15X + 5Y < 75
10X + 6Y < 60
X + Y < 8
X, Y „d 0
a. Set up and solve using Lindo.
b. What are the values of X and Y at the optimal solution?
c. What is the optimal value of the objective function?
5. Use this graph to answer the questions.
Max 20X + 10Y
s.t. 12X + 15Y < 180
15X + 10Y < 150
3X - 8Y < 0
X , Y > 0
a. Which area (I, II, III, IV, or V) forms the feasible region?
b. Which point (A, B, C, D, or E) is optimal?
c. Which constraints are binding?
d. Which slack variables are zero?
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