The following linear programming problem has been solved by the management scientist Use the output to answer the questions LINEAR PROGRAMMING PROBELM MAX 25x1 30x2 15x3 s t 4x1 5x2 8x3 1200 9x1 15x2 3x3 1500 OPTIMAL SOLUTION objective Function Value 4700 000 variable value reduced costs x1 140 000 0 000 x2 0 000 10 000 x3 80 000 0 000 constraint slack surplus dual prices 1 0 000 1 000 2 0 000 2 333 OBJECTIVE COEFFICIENT RANGES variable lower limit current value upper limit x1 19 286 25 000 45 000 x2 no 30 000 40 000 x3 8 333 15 000 50 000 RIGHT HAND SIDE RANGES constraint lower limit current value upper limit 1 666 667 1200 000 4000 000 2 450 000 1500 000 2700 000 a give the complete optimal solution b which constraints are binding c what is the dual price for the second constraint what interpretation does this have d over what range can the objective function coefficient of x2 vary before a new solution point becomes optimal e by how much can the amount of resource 2 decrease before the dual price will change

Question: The following linear programming problem has been solved by the management scientist. Use the output to answer the questions. LINEAR PROGRAMMING PROBELM MAX 25x1 +

The following linear programming problem has been solved by the management scientist. Use the output to answer the questions.

LINEAR PROGRAMMING PROBELM

MAX 25x1 + 30x2 + 15x3

s.t.

4x1 + 5x2 + 8x3 < 1200
9x1 + 15x2 + 3x3 < 1500

OPTIMAL SOLUTION
objective Function Value = 4700.000

variable	value	reduced costs
x1	140.000	0.000
x2	0.000	10.000
x3	80.000	0.000

constraint	slack/surplus	dual prices
1	0.000	1.000
2	0.000	2.333

OBJECTIVE COEFFICIENT RANGES

variable	lower limit	current value	upper limit
x1	19.286	25.000	45.000
x2	no	30.000	40.000
x3	8.333	15.000	50.000

RIGHT HAND SIDE RANGES

constraint	lower limit	current value	upper limit
1	666.667	1200.000	4000.000
2	450.000	1500.000	2700.000

a. give the complete optimal solution

b. which constraints are binding?

c. what is the dual price for the second constraint? what interpretation does this have?

d. over what range can the objective function coefficient of x2 vary before a new solution point becomes optimal?

e. by how much can the amount of resource 2 decrease before the dual price will change?

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