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