SOLVED

21) A maximizing linear programming problem has two constraints: 2X + 4Y ≤ 100 and 3X + 10Y ≤ 210, in addition to constraints stating that both X and Y must be nonnegative. What are the corner points of the feasible region of this problem? A) (0, 0), (50, 0), (0, 21), and (20, 15) B) (0, 0), (70, 0), (25, 0), and (15, 20) C) (20, 15) D) (0, 0), (0, 100), and (210, 0) E) (0, 0), (0, 25), (50, 0), (0, 21), and (70, 0) 22) A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is TRUE? A) There are four corner points including (50, 0) and (0, 12.5). B) The two corner points are (0, 0) and (50, 12.5). C) The graphical origin (0, 0) is not in the feasible region. D) The feasible region includes all points that satisfy one constraint, the other, or both. E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. 23) A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is TRUE? A) There are four corner points including (50, 0) and (0, 12.5). B) The two corner points are (0, 0) and (50, 12.5). C) The graphical origin (0, 0) is in the feasible region. D) The feasible region is triangular in shape, bounded by (50, 0), (33.3333, 8.3333), and (100, 0). E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. 24) A linear programming problem has three constraints, plus nonnegativity constraints on X and Y. The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 6X + 3Y ≤ 90. What is the largest quantity of X that can be made without violating any of these constraints? A) 50 B) 30 C) 20 D) 15 E) 10 25) Suppose that an iso-profit line is given to be X + Y = 10. Which of the following represents another iso-profit line for the same scenario? A) X + Y = 15 B) X – Y = 10 C) Y – X = 10 D) 2X + Y = 10 E) none of the above 26) Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $2Y what is the maximum profit the company can earn? A) $0 B) $10 C) $15 D) $14 E) $24 27) Suppose that the feasible region of a maximization LP problem has corners of (0,0), (5,0), and (0,5). How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X + 5Y? A) 0 B) 1 C) 2 D) 5 E) Infinite 28) Which of the following correctly describes all iso-profit lines for an LP maximization problem? A) They all pass through the origin B) They are all parallel. C) They all pass through the point of maximum profit. D) Each line passes through at least 2 corners. E) all of the above 29) A linear programming problem has three constraints, plus nonnegativity constraints on X and Y. The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints? A) 50 B) 30 C) 20 D) 15 E) 10 30) Consider the following constraints from a two-variable linear program:X ≥ 1;Y ≥ 1;X + Y ≤ 9. If these are the only constraints, which of the following points (X, Y) CANNOT be the optimal solution? A) (1, 1) B) (1, 8) C) (8, 1) D) (4, 4) E) The question cannot be answered without knowing the objective function. 31) The ________ is the set of all feasible combinations of the decision variables. 32) Two methods of solving linear programming problems by hand include the corner-point method and the ________. 33) What is the feasible region in a linear programming problem?