document.write( "Question 1201321: A division of the Winston Furniture Company manufactures dining tables and chairs. Each table requires 40 board feet of wood and 6 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. The profit for each table is $45, and the profit for each chair is $25. In a certain week, the company has 3200 board feet of wood available and 520 labor-hours available. How many tables and chairs should Winston manufacture to maximize its profit?
\n" ); document.write( "tables: ?
\n" ); document.write( "chairs: ?\r
\n" ); document.write( "\n" ); document.write( "What is the maximum profit? \n" ); document.write( "
Algebra.Com's Answer #835649 by Theo(13342)\"\" \"About 
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x = number of dining tables.
\n" ); document.write( "y = number of chairs.
\n" ); document.write( "constraints:
\n" ); document.write( "40x + 16y <= 3200
\n" ); document.write( "6x + 4y <= 520
\n" ); document.write( "x >= 0
\n" ); document.write( "y >= 0
\n" ); document.write( "objective function:
\n" ); document.write( "maximize 45x + 25y
\n" ); document.write( "graph oppositve of constraints.
\n" ); document.write( "unshaded area is region of feasibility.
\n" ); document.write( "evaluate objective function at corner points of feasible region.
\n" ); document.write( "find coordinate points where profit is maximum.
\n" ); document.write( "that's your solution.
\n" ); document.write( "maximum profit is at (70,25) = 70 * 45 + 25 * 25 = 3775
\n" ); document.write( "that's 70 tables and 25 chairs.
\n" ); document.write( "constraints are satisfied because:
\n" ); document.write( "70 * 40 + 25 * 16 = 3200 which is <= 3200
\n" ); document.write( "70 * 6 + 25 * 4 = 520 which is <= 520
\n" ); document.write( "here's the graph.
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