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
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 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?

Question

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?

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 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?

Quizplus · Accepted Answer

The Answer of 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 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 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?

Consider the Following Linear Program