I'm having trouble setting up the variables and constraints in these questions. Wondering if someone can help? Thanks!

http://img216.imageshack.us/img216/6991/2zq1.jpg

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- Aug 11th 2006, 09:50 AMclassicstringsApplications of Linear Programming
I'm having trouble setting up the variables and constraints in these questions. Wondering if someone can help? Thanks!

http://img216.imageshack.us/img216/6991/2zq1.jpg - Aug 11th 2006, 09:36 PMSoroban
Hello, classicstrings!

Here's the second one . . .

Quote:

A furniture maker produces cupboards and bookshelves.

Both products use wooden planks, sawing time, sanding time, and assembly time.

The cupboards use 20 m of wood, 40 minutes of sawing, 60 minutes of sanding,

and 10 minute of assembly time for a profit of $280.

The bookshelves use 10 m of wood, 30 minutes of sawing, 90 minutes of sanding,

and 30 minutes of assembly time for a profit of $340.

There are 220 m of wood, 480 minutes of sawing time, 1080 minutes of sanding time,

and 330 minutes of assembly time available.

How many of each item should be made for maximum profit?

Let = number of cupboards, = number of bookshelves. .**[1]**

A chart helps to organize the information . . .Code:`| wood + saw | sand | assem |`

- - - - - - - - + - - -+ - - + - - -+ - - - +

cupboards (x) | 20x | 40x | 60x | 10x |

- - - - - - - - + - - + - - + - - -+ - - - +

bookshelves (y) | 10y | 30y | 90y | 30y |

- - - - - - - - + - - + - - + - - -+ - - - +

available | 220 | 480 | 1080 | 330 |

- - - - - - - - + - - -+ - - + - - -+ - - - +

Wood: .**[2]**

Sawing: .**[3]**

Sanding: .**[4]**

Assembly: .**[5]**

**[1]**places us in Quadrant 1.

**[2]**Graph the__line__: . .It has intercepts: . .

. . .Shade the region below the line.

**[3]**Graph the line: . .It has intercepts:

. . .Shade the region below the line.

**[4]**Graph the line: . .It has intercepts:

. . .Shade the region below the line.

**[5]**Graph the line: . .It has intercepts:

. . .Shade the region below the line.

The final region is a hexagon. .Its vertices are (clockwise from the origin):

. .

Test them in the profit function:

. . to see which one produces maximum profit.

- Aug 13th 2006, 02:09 AMclassicstrings
Hey Soroban! You have done the harder one for me, and I have gone through it a couple of times myself after, I have done the first one by looking @ how you did them. Cheers!