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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?

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.