document.write( "Question 127434: 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 tables will result in a profit of $20 each. How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach. \n" ); document.write( "
Algebra.Com's Answer #93448 by ankor@dixie-net.com(22740)\"\" \"About 
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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 tables will result in a profit of $20 each. How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach.
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of picnic tables
\n" ); document.write( "Let y = no. of benches
\n" ); document.write( ":
\n" ); document.write( "The labor constraint:
\n" ); document.write( "6x + 4y <= 1200
\n" ); document.write( "4y <= 1200 - 6x; divide equation by 4
\n" ); document.write( "y <= 300 - 1.5x
\n" ); document.write( ":
\n" ); document.write( "Plot above equation for x = 0 and x = 60
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( " 0 | 300
\n" ); document.write( "60 | 210
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "The material constraint
\n" ); document.write( "35x + 10y <= 3500
\n" ); document.write( "10y <= 3500 - 35x
\n" ); document.write( "y <= 350 - 3.5x; divide equation by 10
\n" ); document.write( ":
\n" ); document.write( "Plot the above equation for x = 0 and x = 60
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( " 0 | 350
\n" ); document.write( "60 | 140
\n" ); document.write( ":
\n" ); document.write( "Graph will look like this
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-50%2C+150%2C+-100%2C+400%2C+300-1.5x%2C+350-3.5x%29+\"
\n" ); document.write( "The area of feasibility is at or below the two graphs, which ever is lowest
\n" ); document.write( "Area is bounded by coordinates; 0,0; 0,300; 100,0; and an integer values of 25, 262
\n" ); document.write( "Find the profit using each:
\n" ); document.write( "Tables + Benches
\n" ); document.write( "20(0) + 9(300) = $2700
\n" ); document.write( "20(100) + 9(0) = $2000
\n" ); document.write( "20(25) + 9(262) = $2858;
\n" ); document.write( ":
\n" ); document.write( "25 tables and 262 benches will yield max profit;
\n" ); document.write( "utilizes:
\n" ); document.write( "6(25) + 4(262) = 1190 hrs of labor
\n" ); document.write( "35(25) + 10(262) = 3495 ft of red-wood
\n" ); document.write( ":
\n" ); document.write( "This is the general idea. Check my math here, a lot of chance for mistakes \n" ); document.write( "
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