Consider the following linear program: Max 3A + 2B s.t. 1A + 1B 39 3A + 1B S 24 1A + 2B 3 16 A, B 2 0 The value of the optimal solution is 25.5. Suppose that the right-hand side of the constraint 1 is increased from 9 to 10. a. Use the graphical solution procedure to find the new optimal solution. B (1) B 26 26 (ii) 24 24- 22 22 20 20 18 18 16 16+ 14 14 12 Optimal Solution A = 0, B = 8 3A + 2B = 16 12 10 10- 8 8 Optimal Solution A= 6.4, B = 4.8 3A + 2B = 28.8 6 6 4 4 2 2 A 2 HA 16 18 20 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 B B (iv) 26+ 24 22+ 20 18+ 16+ 26+ 24 22+ 20+ 18-1 16+ 14 12 10+ 14 12 10+ 8 8 Optimal Solution A=7, B = 3 3A + 2B = 27 Optimal Solution A = 10, B=0 3A + 2B = 30 6 6 4 4 2- 2 A A 24 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 Graph (iii) b. Use the solution to part (a) to determine the dual value for constraint 1. If required, round your answer to 1 decimal place. Dual Value: 1.5 c. The computer solution for the linear program in Problem 1 provides the following right-hand-side range information: RHS Constraint 1 2. 3 Value 9.00000 24.00000 16.00000 Allowable Increase 2.20000 3.00000 Infinite Allowable Decrease 1.00000 11.00000 5.50000 What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1? If required, round your answers to five decimal places. c. The computer solution for the linear program in Problem 1 provides the following right-hand-side range information: RHS Constraint Value 1 Allowable Increase 2.20000 3.00000 Infinite 9.00000 24.00000 16.00000 Allowable Decrease 1.00000 11.00000 5.50000 2 3 What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1? If required, round your answers to five decimal places. The right-hand-side range for constraint 1 is 8 to 11.2 . As long as the right-hand side stays within this range, the dual value is applicable d. The dual value for constraint 2 is 0.5. Using this dual value and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2? If required, round your answers to 1 decimal place. The improvement in the value of the optimal solution will be 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is between and