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## Homework Statement

A birchwood table company has an individual who does all its finishing

work and it wishes to use him in this capacity at least 36 hours each

week. By union contract, the assembly area can be used at most 48 hours

each week. The company has three models of birch tables, T1, T2 and T3.

T1 requires 1 hour for assembly, 2 hours for finishing, and 9 board feet of

birch. T2 requires 1 hour for assembly, 1 hour for finishing and 9 board

feet of birch. T3 requires 2 hours for assembly, 1 hour for finishing and 3

board feet of birch. Write a LOP that will compute how many of each model

should be made in order to minimize the board feet of birchwood used.

**2. What I want to do with this problem**

Here is the thing, I wrote out the equations, but my variables don't mean a thing. I tried to make some sense out of it

Here is the equations

[tex]1x_1 + 1x_2 +2x_3 \leq 48[/tex]

[tex]2x_1 + 1x_2 +1x_3 \geq 36[/tex]

[tex]P = 9x_1 + 9x_2 + 3x_3[/tex]

[tex]x_1, x_2, x_3 \geq 0[/tex]

For instance the first equation is

[tex]1x_1 + 1x_2 +2x_3 \leq 48[/tex]

Right hand side is hours, so I expect the units on [tex]1x_1 + 1x_2 +2x_3[/tex] cancel out so that it gives me hours too

Look at the coefficients of [tex]1x_1 + 1x_2 +2x_3[/tex]

The "1" in front of [tex]x_1[/tex] represents "hour for assembly" or "hour/assembly". So to make things work out, [tex]x_1[/tex] has units "assembly for T_1[/tex]"

But that doesn't work for the second equation because I will need [tex]x_1[/tex] to have units "finishing for T_1[/tex]"

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