Woody, a character in the Year 1 unit Shadows, is very interested in

trees, especially measuring them. Well, he has developed his hobby into

a trade and is opening a carpentry shop that makes tables and chairs.

The wood Woody buys is sold in terms of a unit called a board foot,

which is based on boards with a thickness of 1 inch and a width of

1 foot. For example, a board 9 feet long, 1 inch thick, and 1 foot wide

consists of 9 board feet of lumber.

Woody has found that each chair requires 3 board feet of lumber

and 2 hours of labor. Each table requires 7 board feet of lumber and

8 hours of labor. His profit on each chair is $15, and his profit on each

table is $45.

This week, Woody has 420 board feet of lumber and 400 hours of labor

available. He wants to know how

many chairs and how many tables he should make to maximize his profit.

Solve this problem using the general strategy for working on linear

programming problems without drawing a feasible region. Use C for the

number of chairs Woody makes and T for the number of tables. Explain

your work carefully. If you discover places where the strategy is unclear

or doesn't seem to work correctly, make a note of them.