Suffolk Manufacturing produces three types of paneling from Pine and Spruce. The
ID: 357018 • Letter: S
Question
Suffolk Manufacturing produces three types of paneling from Pine and Spruce. The types of paneling are Western (X1), Old English (X2), and Colonial (X3). Each sheet must be cut and pressed. The resource requirements are given in the following linear programming formulation.
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 an additional hour of cutting? Over what range is this value valid?
Maximize Z = 4X1 + 10X2 + 8X3 (profit, $)
Variable Value Reduced Cost Original Val Lower Bound Upper Bound
X1 0 2 4 -Infinity 6
X2 10 0 10 4 16
X3 20 0 8 5 20
Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound
Pine 0 80 200 120 Infinity
Spruce 0 70 160 90 Infinity
Cutting 2 0 50 20 80
Pressing 2 0 80 50 132.5
Explanation / Answer
a) Spruce ---> Marginal Value = Slack/Surplus = 70 per unit. Valid for 90 to Infinity
b) Cutting ---> Marginal Value = Slack/Surplus = 0 per unit. Valid for 20 to 80
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