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, $)
ST 5X1 + 4X2 + 4X3\leq 200 (pine, lb)
2X1 + 5X2 + 2X3\leq 160 (spruce, lb)
1X1 + 1X2 + 2X3\leq 50 (cutting, hr)
2X1 + 4X2 + 2X3\leq 80 (pressing, hr)
X1 + X2 + X3\geq 0

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being born in poverty would limit the people's chances, opportunities and benefits.

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- rich people tend to have more capital in their disposal. this would benefit them in business since it is far easier for them to fund their business operation compared to poor people.

answerproduct line length; product mix width;