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A furniture company is producing two types of furniture. Product A requires 8 board feet of...

A furniture company is producing two types of furniture. Product A requires 8 board feet of wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are 2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit. Formulate the problem as a linear program.

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Answer #1

Let "x" be the number of units of type A furniture produced.

"y" be the number of units of type B furniture produced.

Given product A requires 8 board feet of wood and 2 lbs of wicker.

Product B requires 6 board feet of wood and 6 lbs of wicker.

The availability of wood is 2000 board feet and 1000 lbs of wicker.

The given information is summarize as:

Product A(x) Product B(y) Availability

Wood 8x 6y 2000

wicker 2x 6y 1000

The profit margin on product A is $30 while on product B it is $40

Therefore we want to optimize (maximize) objective function:

Z=30x+40y

With respect to constraints

such that:

,

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