Tiêu đề LINEAR PROGRAMMING.pdf ✅

CHAPTER 12 LINEAR PROGRAMMING Exercise 1: NCERT Based Topic-wise MCQs 12.1 & 12.2 INTRODUCTION, LINEAR PROGRAMMING PROBLEMS AND ITS MATHEMATICAL FORMULATION 1. L.P.P is a process of finding NCERT Page-504/N-394 (a) Maximum value of objective function (b) Minimum value of objective function (c) Optimum value of objective function (d) None of these 2. L.P.P. has constraints of NCERT Page-505/N-395 (a) one variables (b) two variables (c) one or two variables (d) two or more variables 3. Corner points of feasible region of inequalities gives NCERT Page-507/N-394 (a) optional solution of L.P.P. (b) objective function (c) constraints. (d) linear assumption 4. Which of these terms is not used in a linear programming problem? NCERT Page-504/N-394 (a) Slack variables (b) Objective function (c) Concave region (d) Feasible solution 5. The optimal value of the objective function is attained at the points NCERT Page-508/N-395 (a) Given by intersection of inequations with axes only (b) Given by intersection of inequations with x-axis only (c) Given by corner points of the feasible region (d) None of these 6. If the constraints in a linear programming problem are changed NCERT Page-507/N-395 (a) The problem is to be re-evaluated (b) Solution is not defined (c) The objective function has to be modified (d) The change in constraints is ignored 7. Which of the following statements is correct? NCERT Page-505/N-395
(a) Every L.P.P. admits an optimal solution (b) A L.P.P. admits a unique optimal solution (c) If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions (d) The set of all feasible solutions of a L.P.P. is not a convex set. 8. The constraints −x1 + x2 ≤ 1, −x1 + 3x2 ≤ 9, x1, x2 ≥ 0 define on NCERT Page-507/N-395 (a) Bounded feasible space (b) Unbounded feasible space (c) Both bounded and unbounded feasible space (d) None of these 9. A vertex of bounded region of inequalities x ≥ 0, x + 2y ≥ 0 and 2x + y ≤ 4 is NCERT Page-507/N-395 (a) (1,1) (b) (0,1) (c) (3,0) (d) (0,1) 10. The inequalities 5x + 4y ≥ 20, x ≤ 6, y ≤ 4 form NCERT Page-507/N-395 (a) A square (b) A rhombus (c) A triangle (d) A quadrilateral 11. The maximum vale of P = x + 3y such that 2x + y ≤ 20, x + 2y ≤ 20x ≥ 0, y ≥ 0 is (a) 10 NCERT Page-511/N-401 (b) 60 (c) 30 (d) None 12. Which of the following is not a vertex of the positive region bounded by the inqualities 2x + 3y ≤ 6,5x + 3y ≤ 15 and x, y ≥ 0 NCERT Page-511/N-401 (a) (0,2) (b) (0,0) (c) (3,0) (d) None 13. If a point (h, k) satisfies an inequation ax + by ≥ 4 then the half plane represented by the inequation is (a) The half plane containing the point (h, k) but excluding the points on ax + by = 4 (b) The half plane containing the point (h, k) and the points on ax + by = 4 (c) Whole xy-plane (d) None of these 14. Inequation y − x ≤ 0 represents (a) The half plane that contains the positive x-axis (b) Closed half plane above the line y = x which contains positive y-axis (c) Half plane that contains the negative x-axis (d) None of these 15. Corner points of feasible region of inequalities gives NCERT Page-506/N-399 (a) optimal solution of L.P.P. (b) objective function
(c) constraints. (d) linear assumption 16. The solution set of constraints x + 2y ≥ 11,3x + 4y ≤ 30, 2x + 5y ≤ 30 and x ≥ 0, y ≥ 0, includes the point NCERT Page-507/N-399 (a) (2,3) (b) (3,2) (c) (3,4) (d) (4,3). 17. For the following feasible region, the linear constraints are NCERT Page-507/N-401 (a) x ≥ 0, y ≥ 0,3x + 2y ≥ 12, x + 3y ≥ 11 (b) x ≥ 0, y ≥ 0,3x + 2y ≤ 12, x + 3y ≥ 11 (c) x ≥ 0, y ≥ 0,3x + 2y ≤ 12, x + 3y ≤ 11 (d) None of these 18. Maximize Z = 8x + 7y subject to constraints 3x + y ≤ 66, x + y ≤ 45, x ≤ 20, y ≤ 40, x, y ≥ 0 NCERT Page-507/N-401 (a) 305.5 (b) 315.5 (c) 325.5 (d) 335.5 19. Inequations 3x − y ≥ 3 and 4x − y ≥ 4 NCRTS Page-507/N-401 (a) Have solution for positive x and y (b) Have no solution for positive x and y (c) Have solution for all x (d) Have solution for all y 20. The true statement for the graph of inequations 3x + 2y ≤ 6 and 6x + 4y ≥ 20, is (a) Both graph are disjoint (b) Both do not contain origin (c) Both contain point (1,1) (d) None of these 21. The coordinates of the point for minimum value of z = 7x − 8y, subject to the condition x + y ≤ 20, y ≥ 5, x ≥ 0, y ≥ 0 is NCERT Page-509/N-401 (a) (20,0) (b) (15,5)
(c) (0,5) (d) (0,20) 22. Shaded region is represented by NCERT Page-507/N-399 (a) 4x − 2y ≤ 3 (b) 4x − 2y ≤ −3 (c) 4x − 2y ≥ 3 (d) 4x − 2y ≥ −3 23. The maximum value of z = 5x + 2y subject to constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 (a) 10 NCERT Page-507/ N-401 (b) 26 (c) 35 (d) 70 24. Minimum value of Z = 3x + 5y subject to constraints x + y ≥ 2, x + 3y ≥ 3, x, y ≥ 0 (a) 6 NCERT Page-507/N-401 (b) 7 (c) 8 (d) 9 25. The maximum vale of P = x + 3y such that 2x + y ≤ 20, x + 2y ≤ 20, x ≥ 0, y ≥ 0 is (a) 10 NCERT Page-509/N-401 (b) 60 (c) 30 (d) None 26. Shaded region is represented by NCERT Page-507/N-401 (a) 2x + 5y ≥ 80, x + y ≤ 20, x ≥ 0, y ≤ 0