document.write( "Question 1171978: The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 6 hours of wiring and 1 hours of drilling. Each fan must go through 2 hours of wiring and 1 hours of drilling. During the next production period, 240 hours of wiring time are available and up to 77 hours of drilling time may be used. Each air conditioner sold yields a profit of $20. Each fan assembles may be sold for a $15 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graph approach \n" ); document.write( "
Algebra.Com's Answer #797358 by Theo(13342)\"\" \"About 
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set up a table as shown beloow:
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document.write( "                              x                   y\r\n" );
document.write( "                      air conditioner            fan\r\n" );
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document.write( "wiring                        6                   1           <= 240\r\n" );
document.write( "drilling                      2                   1           <= 77\r\n" );
document.write( "profit                        25                  15          maximize\r\n" );
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\n" ); document.write( "\n" ); document.write( "your objective function is 25x + 15y.
\n" ); document.write( "this is what you want to maximize.\r
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\n" ); document.write( "\n" ); document.write( "your constraint functions are:
\n" ); document.write( "6x + y <= 240
\n" ); document.write( "2x + y <= 77
\n" ); document.write( "x >= 0
\n" ); document.write( "y >= 0\r
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\n" ); document.write( "\n" ); document.write( "using the desmos.com calculator, you will graph the opposite of the contsraint functions.
\n" ); document.write( "the area on the graph that is not shaded is your region of feasibiliy.
\n" ); document.write( "your maximum profit will be at the corner points of the feasible region.
\n" ); document.write( "you find the maximum profit by evaluating the objective function at each of the corner points.\r
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\n" ); document.write( "\n" ); document.write( "the graph looks like this.\r
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\n" ); document.write( "\n" ); document.write( "total profit is shown below with all constraints met.\r
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document.write( "x	y	drill	wire	profit\r\n" );
document.write( "0	77	154	77	1155\r\n" );
document.write( "21.5	55.5	240	77	1370\r\n" );
document.write( "40	0	240	40	1000\r\n" );
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\n" ); document.write( "\n" ); document.write( "total drill hours are less than or equal to 240
\n" ); document.write( "total wire hours are less than or equal to 77
\n" ); document.write( "maximum total profit is 1370 when x = 21.5 and y = 55.5\r
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