Hello, classicstrings!

Here's the second one . . .

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):

. . 6,8),\;(9,4),\;(0,11)" alt="(0,0),\;(0,11),\;(3,10),\6,8),\;(9,4),\;(0,11)" />

Test them in the profit function:

. . to see which one produces maximum profit.