Solved

Consider the Following Linear Program

Question 41

Essay

Consider the following linear program:
MIN 6x1 + 9x2 ($ cost)
s.t.x1 + 2x2 < 8
10x1 + 7.5x2 > 30
x2 > 2
x1,x2 > 0
The Management Scientist provided the following solution output:
OPTIMAL SOLUTION
Objective Function Value = 27.000
Consider the following linear program: MIN 6x<sub>1</sub> + 9x<sub>2</sub> ($ cost) s.t.x<sub>1</sub> + 2x<sub>2</sub> < 8 10x<sub>1</sub> + 7.5x<sub>2</sub> > 30 x<sub>2</sub> > 2 x<sub>1</sub>,x<sub>2</sub> > 0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES a.What is the optimal solution including the optimal value of the objective function? b.Suppose the unit cost of x<sub>1</sub> is decreased to $4.Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4? c.How much can the unit cost of x<sub>2</sub> be decreased without concern for the optimal solution changing? d.If simultaneously the cost of x<sub>1</sub> was raised to $7.5 and the cost of x<sub>2</sub> was reduced to $6,would the current solution still remain optimal? e.If the right-hand side of constraint 3 is increased by 1,what will be the effect on the optimal solution? Consider the following linear program: MIN 6x<sub>1</sub> + 9x<sub>2</sub> ($ cost) s.t.x<sub>1</sub> + 2x<sub>2</sub> < 8 10x<sub>1</sub> + 7.5x<sub>2</sub> > 30 x<sub>2</sub> > 2 x<sub>1</sub>,x<sub>2</sub> > 0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES a.What is the optimal solution including the optimal value of the objective function? b.Suppose the unit cost of x<sub>1</sub> is decreased to $4.Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4? c.How much can the unit cost of x<sub>2</sub> be decreased without concern for the optimal solution changing? d.If simultaneously the cost of x<sub>1</sub> was raised to $7.5 and the cost of x<sub>2</sub> was reduced to $6,would the current solution still remain optimal? e.If the right-hand side of constraint 3 is increased by 1,what will be the effect on the optimal solution? OBJECTIVE COEFFICIENT RANGES
Consider the following linear program: MIN 6x<sub>1</sub> + 9x<sub>2</sub> ($ cost) s.t.x<sub>1</sub> + 2x<sub>2</sub> < 8 10x<sub>1</sub> + 7.5x<sub>2</sub> > 30 x<sub>2</sub> > 2 x<sub>1</sub>,x<sub>2</sub> > 0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES a.What is the optimal solution including the optimal value of the objective function? b.Suppose the unit cost of x<sub>1</sub> is decreased to $4.Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4? c.How much can the unit cost of x<sub>2</sub> be decreased without concern for the optimal solution changing? d.If simultaneously the cost of x<sub>1</sub> was raised to $7.5 and the cost of x<sub>2</sub> was reduced to $6,would the current solution still remain optimal? e.If the right-hand side of constraint 3 is increased by 1,what will be the effect on the optimal solution? RIGHT HAND SIDE RANGES
Consider the following linear program: MIN 6x<sub>1</sub> + 9x<sub>2</sub> ($ cost) s.t.x<sub>1</sub> + 2x<sub>2</sub> < 8 10x<sub>1</sub> + 7.5x<sub>2</sub> > 30 x<sub>2</sub> > 2 x<sub>1</sub>,x<sub>2</sub> > 0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES a.What is the optimal solution including the optimal value of the objective function? b.Suppose the unit cost of x<sub>1</sub> is decreased to $4.Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4? c.How much can the unit cost of x<sub>2</sub> be decreased without concern for the optimal solution changing? d.If simultaneously the cost of x<sub>1</sub> was raised to $7.5 and the cost of x<sub>2</sub> was reduced to $6,would the current solution still remain optimal? e.If the right-hand side of constraint 3 is increased by 1,what will be the effect on the optimal solution?
a.What is the optimal solution including the optimal value of the objective function?
b.Suppose the unit cost of x1 is decreased to $4.Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4?
c.How much can the unit cost of x2 be decreased without concern for the optimal solution changing?
d.If simultaneously the cost of x1 was raised to $7.5 and the cost of x2 was reduced to $6,would the current solution still remain optimal?
e.If the right-hand side of constraint 3 is increased by 1,what will be the effect on the optimal solution?

Correct Answer:

verifed

Verified

a.x1 = 1.5 and x2 = 2.0,and the objective ...

View Answer

Unlock this answer now
Get Access to more Verified Answers free of charge

Related Questions

Q20: When the cost of a resource is

Q21: In a linear programming problem,the binding constraints

Q24: A constraint with a positive slack value<br>A)will

Q29: If the dual price for the right-hand

Q31: Which of the following is not a

Q36: A section of output from The Management

Q37: Portions of a Management Scientist output are

Q43: Consider the following linear program:<br>MAX 3x<sub>1</sub> +

Q43: The dual price measures, per unit increase

Q44: There is a dual price for every