\f\f\f7.2)Maximize 8 x 7 y Subject to - 3 x y 13 (1) 5 x 3 y 27 (2) x y 3 (3) x 0 ( 4) y 0 (5) Series 1 is: Series 2 is: Series 3 is: Series 4 is: Series 5 is: 3 x y 13 5 x 3 y 27 x y 3 x 0 y 0 The boundaries and the inside portion of the shaded region is the solution set. The vertices(corner points)are (13/3, 0), (0, 9),(0,3) and (3,4) Value of the objective function at (13/3, 0) is 8x13/3 + 7x0 =104/3 = 34 Value of the objective function at (3, 4) is 8x 3+7x 4= 52 Value of the objective function at (0, 9) is 8 x0+7x 9=63 Thus the optimal solution is 63 7.1) a) True b) False c) True 7.3) a) Objective function is Maximize 100 x 120 y Therefore option (b) is correct. 2 ~ 34.667 3 b) Option (C) is correct. 3x y 450 represents the availability of metal A c) Option(D) is correct. x 2 y 300 represents the availability of metal B d) ) Option(E) is correct. y 50 represents the minimum requirement of invincible blue suits. e) Option (f) is correct. x 0 is the constraint. Therefore the linear program is Maximize 100 x 120 y Subject to - 3x y 450 -------------------(1) x 2 y 300 ------------------(2) y 50 ------------------------------(3) x 0 ------------------------------(4) Shaded portion represents the feasible region. The two vertices are (400/3, 50) and (120, 90) We get the maximum profit at (120, 90)therefore it gives the optimal solution. f) The maximum profit is 100x120+120 x90=22800 pounds 7.4) a) Option (F) is correct. Maximize 6 x 4 y is the objective function. b) Option (C) is correct. Constraint 120 x 160 y 1800 represents minimum revenue requirement. c) Option (D) is correct. Constraint x 10 represents the maximum rafts available. d) Option (F) is correct. The constraint 6 x 30 represents the demand of raft trips should be satisfied. e) Option (A) is correct. The constraint x y 12 represents the maximum number of captains who can be deployed