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Exercises for Linear Programming (Cht. 7) BSNS2120, J. Wang 1. There is one, and only one, objective function in a linear program. a. True b. False 2. Which are the non-negative constraints of a linear program? a. X1, X2 >0 b. X1, X2>=0 c. X1+X2>0 d. X1+X2>=0 3. Every linear program has "non-negative constraints". a. True b. False 4. Equation X1+2X2=5 corresponds to a __________ in a two-dimensional coordinate system. a. point b. straight line c. circle d. parabola 5. In a linear program, number of variables must be less than number of constraints. a. True b. False 6. A constraint must be an inequality (either "<=" or ">="). A constraint cannot be an equation ("="). a. True b. False 7. A solution is feasible if it makes a. all the constraints hold. b. at least one constraint hold. 8. RHS stands for "right-hand-side". a. True b. False 9. There is no variable term in RHS. a. True b. False 10. Does (X1=2, X2=1) satisfy the constraint 2X1-3X2<=2? a. Yes b. No 11. Is (X1=5, X2=10) feasible to the LP {Min X1+X2, s.t. X1+0.4X2>=5, X1+X2>=8)? a. Yes b. No 12. If a linear program is infeasible then a. the objective function value can be as large as possible in the feasible region. b. the feasible region is empty. c. there is no feasible solution at all for this program. d. there is no solution satisfying all the constraints. e. All of b, c, and d. 13. _______ shows the change of the objective function value due to a unit increase of a RHS: a. Optimal range b. Shadow price c. Feasible solution d. Sensitivity range 14. Linear program {Max 3X1+2X2, s.t. X1+X2>=10} a. is infeasible. b. has unbounded optimal solution. c. has multiple optimal solution. d. (X1=10,000, X2=20,000) is the optimal solution. 15. Suppose (X1=3, X2=1) is a feasible solution of a linear program. If the linear program’s objective function changes while its constraints remain unchanged, then, in the new linear program, a. (X1=3, X2=1) is no longer a feasible solution. b. (X1=3, X2=1) is still a feasible solution. c. Neither of above. (X1=3, X2=1) can be, or can be not, a feasible solution. 16. The sensitivity range of the RHS of a constraint tells that if the RHS value changes within the range then a. the optimal solution remains unchanged. b. the optimal objective function value remains unchanged. c. the shadow prices (i.e., dual values) remain unchanged. 17. The sensitivity range of an objective function coefficient tells that if the coefficient changes within the range then a. the optimal solution remains unchanged. b. the optimal objective function value remains unchanged. c. the shadow prices (i.e., dual values) remain unchanged. 18. Suppose the optimal objective function value of a maximization linear program problem is 470. Suppose X=(X1=5, X2=7) is a feasible solution of the same linear program, but it is not optimal. Let Z denote the objective function value associated with X. Then a. Z<470. b. Z>470. c. Z=470. d. Given information is not sufficient to decide. 19. If the dual value of processing hours is $15 in a product mix linear program in which profit is maximized, then it means that a. workers should all be paid at $15 per hour. b. an additional processing hour would bring $15 more profit for the company. c. an additional processing hour would cost the company $15. 20. The shadow prices of constraints are found in the column of _________ in the result of QM. a. RHS b. Dual c. any variable 21. Suppose a maximization linear program is infeasible. If we change the objective from maximization to minimization, then it is still infeasible. a True b. False Answers: 1.a 2.b 3.a 4.b 5.b 6.b 7.a 8.a 9.a 10.a 11.b 12.e 13.b 14.b 15.b 16.c 17.a 18.a 19.b 20.b 21.a