The evergreen products firm produces three types of pressed paneling from pine and spruce. The three types of paneling are wide(x₁), medium (x₂) and small(x₃). Each sheet must be cut and pressed. The resource requirements are given in the following LP formulation.

Maximize Z = 4x₁ + 10x₂+ 8x₃

Subject to:

5x₁ + 4x₂+ 4x₃200 ( pine, lb)

2x₁ + 5x₂+ 2x₃160 ( spruce, lb)

x₁ + x₂+ 2x₃50 ( cutting, hrs)

2x₁ + 4x₂+ 2x₃80 ( pressing, hr)

x₁,x_2,x₃0

The final simplex table for this model is as follows.

4 10 8 0 0 0

Basic variables c_j x₁ x₂ x₃ s₁ s₂s₃ s₄ quantity

s₁ 0 7/3 0 0 1 0 -4/3 -2/3 80

s₂ 0 -1/30 0 0 11/3-4/370

x₃8 1/3 1 0 0 0 2/3 1/6 20

x₂10 1/3 1 0 0 0 -1/3 1/3 10

Z_j 6 10 8 0 0 2 2 260

C_j -Z_j0 0 0 0 0 -2 -2

a. What is the marginal value of an additional pound of spruce? Over what range is this value

valid?

b. What is the marginal value of additional hours of cutting? Over what range is this value

valid?

c. Given a choice between securing more hours and or morepressing hours, which should the

management select?

d. If the amount of the spruce available to the firm were decreased from 160 to 100 pounds, would

this reduction affect the solution? Why? If it is what is the new solution?

e. What unit profit would have to be made from wide paneling before management consider

producing it?

f. Management is considering changing the profit of small paneling from Birr 8 to Birr 13.

would this change affect the solution?