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
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?

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