Question: Consider the following linear program: Max 6 x 1 + 8 x 2 s.t. x 1 6 2 x 1 + 3 x 2 19

Consider the following linear program:

Max 6x1 + 8x2

s.t.
x1 6
2x1 + 3x2 19
x1 + x2 8
x1, x2 0

The graphical solution to the problem is shown below. From the graph, we see that the optimal solution occurs at

x1 = 5, x2 = 3

and obtains a maximum value of 54.

(a)

Calculate the range of optimality for the objective function coefficient for

x1.

(Round your answers to two decimal places.)

Calculate the range of optimality for the objective function coefficient for

x2.

(Round your answers to two decimal places.

(b)

Calculate the dual value for the first constraint.

Calculate the dual value for the second constraint.

Calculate the dual value for the third constraint.

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