sensitivity analysis problem

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The LP problem whose output follows determines how many necklaces (X1), bracelets (X2), rings (X3), and earrings (X4) a jewelry store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions. LINEAR PROGRAMMING PROBLEM MAX 60X1+72X2+90X3+75X4 S.T. 1) X1+2X2+2X3+2x4 120 2) 3X1+5X2+X4 150 3) X1+X3 S 25 4) X2+X3+X4 2 50 OPTIMAL SOLUTION Objective Function Value - 8550.000 Variable Value Reduced Cost X1 20.000 0.000 40.000 50.000 8 X3 X4 0.000 3.000 0.000 0.000 21 Dual Price 45.000 0.000 15.000 - 15.000 24 Constraint Slack/Surplus 1 0.000 2 140.000 3 0.000 4 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit X1 52.500 X2 No Lower Limit 75.000 X4 72.000 Current Value 60.000 72.000 90.000 75.000 Upper Limit No Upper Limit 75.000 97.500 90.000 RIGHT HAND SIDE RANGES 3 Constraint 1 2. 3 4 6 Lower Limit 180.000 110.000 20.000 70.000 Current Value 200.000 250.000 60.000 90.000 Upper Limit 235.000 No Upper Limit 110.000 100.000 9 b. c. d 12 How many necklaces, bracelets, rings, earrings should be stocked? What is the profit? How much space will be left unused? How much time will be used? What will happen to the profit if the amount of space increases by 5 units? What will happen to the profit if the amount of second marketing restriction increases by 10 units? a. [20, 0, 40, 50]: 8550 b. O c. O d. 8555 e. 8540 e 15 a. [60, 72, 90, 75): 8550 b. 140 c. O d. 8555 e. 8540 18 a. [20, 0, 40, 50): 8550 b. 140 c. O d. 8775 e. 8400 21 a. [20, 0, 40, 50); 8550 b. O c. 140 d. 8775 e. 8400 24 a. [20, 0, 40, 50]; 8550 b. O c. 140 d. 8325 e. 8700 a. (20, 0, 40, 50); 8550 b. O c. 140 d. 8775 e. 8700 a. 120, 0, 40, 50]; 8550 b. O c. O d. 8775 e. 8400 MacBook Air + 3 4 % 5 6 & 7 8 9 0 E R T Y U 0 a. b. c. How many necklaces, bracelets, rings, earrings should be stocked? What is the profit? How much space will be left unused? How much time will be used? What will happen to the profit if the amount of space increases by 5 units? What will happen to the profit if the amount of second marketing restriction increases by 10 units? d e a. [20, 0, 40, 50]; 8550 b. O c. O d. 8555 e. 8540 a. [60, 72, 90, 75]; 8550 b. 140 c. O d. 8555 e. 8540 a. [20, 0, 40, 50): 8550 b. 140 c. O d. 8775 e. 8400 a. [20, 0, 40, 50): 8550 b. O c. 140 d. 8775 e. 8400 a. [20, 0, 40, 50): 8550 b. O c. 140 d. 8325 e. 8700 a. [20, 0, 40, 50]; 8550 b. O c. 140 d. 8775 e. 8700 a. [20, 0, 40, 50): 8550 b. O c. O d. 8775 e 8400 a. [20, 0, 40, 50); 8550 b. O c. 140 d. 8555 e. 8540 a. [60, 72, 90, 75]; 8550 b. O c. 140 d. 8325 e. 8700 a. [20, 0, 40, 50); 8550 b. O c. O d. 8325 e. 8700