# Linear Programming: Maximizing Profit for The Outdoor Furniture Corporation

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and table will result in a profit of $20 each. How many benches and table should Outdoor Furniture produce to obtain the largest possible profit?

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#### Solution Preview

We set up a table like this:

Bench Table Total

Time 4x 6y 1200

Wood 10x 35y 3500

So, we can set up the inequalities:

4x + 6y <= 1200

10x + 35y <= 3500

where <= means "less than or equal to"

Of course, x >= 0, and y >= 0

where >= means "greater than or equal to"

Now what?

We need to graph them.

To graph 4x + 6y <= 1200, let's get the x-intercept and the y-intercept:

If x=0, then what's y?

4(0) + 6y = 1200

6y = 1200

y = 200

Therefore, there's a point at (0, 200)

If y=0, then what's x?

4x + 6(0) = 1200

4x = 1200

x = 300

Therefore, there's the other point at (300, 0)

You can plot those two points and draw a line between them. To find out which side of the line to shade in (since it's really an ...

#### Solution Summary

Profit is maximized using linear programming This solution provides step-by-step instructions and calculations for setting up and solving the linear programing problem.