document.write( "Question 88286: HELP PLEASE!!!
\n" ); document.write( "Need to make both airplanes and helicopters
\n" ); document.write( "Can't make more than 50 airplanes and no more than 30 helicopters
\n" ); document.write( "Cost to make airplane - 60,000
\n" ); document.write( "Cost to make helicopter - 90,000
\n" ); document.write( "Budget to spend - 3.6 million
\n" ); document.write( "Need to find Max. profit if get 400,000 for each sirplane sold amd 850,000 for each helicopter sold???
\n" ); document.write( "Also - how many helicopters cam be made
\n" ); document.write( "HELP
\n" ); document.write( "NEED:
\n" ); document.write( "Constraints, object function, and solution
\n" ); document.write( "thanks so much
\n" ); document.write( "lucyloo \n" ); document.write( "
Algebra.Com's Answer #64137 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Need to make both airplanes and helicopters
\n" ); document.write( "Can't make more than 50 airplanes and no more than 30 helicopters
\n" ); document.write( "Cost to make airplane - 60,000
\n" ); document.write( "Cost to make helicopter - 90,000
\n" ); document.write( "Budget to spend - 3.6 million
\n" ); document.write( "Need to find Max. profit if get 400,000 for each sirplane sold amd 850,000 for each helicopter sold???
\n" ); document.write( "Also - how many helicopters cam be made
\n" ); document.write( "HELP
\n" ); document.write( "NEED:
\n" ); document.write( "Constraints, object function, and solution
\n" ); document.write( "thanks so much
\n" ); document.write( "lucyloo
\n" ); document.write( "
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document.write( "Let x = the number of airplanes to make.\r\n" );
document.write( "Let y = the number of helicopters to make.\r\n" );
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document.write( ">>...Can't make more than 50 airplanes...<<\r\n" );
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document.write( "So that says\r\n" );
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document.write( "x < 50\r\n" );
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document.write( ">>...no more than 30 helicopters...<<\r\n" );
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document.write( "y < 30\r\n" );
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document.write( ">>...Cost to make airplane - 60,000...<<\r\n" );
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document.write( "That says \r\n" );
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document.write( "the cost to make the x airplanes is 60000x\r\n" );
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document.write( ">>...Cost to make helicopter - 90,000...<<\r\n" );
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document.write( "That says:\r\n" );
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document.write( "The cost to make y helicopters is 90000y\r\n" );
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document.write( ">>...Budget to spend - 3.6 million...<<\r\n" );
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document.write( "That says \r\n" );
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document.write( "60000x + 90000 < 3600000\r\n" );
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document.write( "So the constraints are:\r\n" );
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document.write( "              x < 50\r\n" );
document.write( "              y < 30\r\n" );
document.write( "60000x + 90000y < 3600000\r\n" );
document.write( "              x > 0\r\n" );
document.write( "              y > 0\r\n" );
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document.write( "Those last two are to prevent the number of \r\n" );
document.write( "planes or helicopters from being negative. \r\n" );
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document.write( "We can simplify \r\n" );
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document.write( " 60000x + 90000 < 3600000\r\n" );
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document.write( "by dividing through by 30000, getting\r\n" );
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document.write( "        2x + 3y < 120\r\n" );
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document.write( "So the constraints are\r\n" );
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document.write( "      x < 50\r\n" );
document.write( "      y < 30\r\n" );
document.write( "2x + 3y < 120\r\n" );
document.write( "      x > 0\r\n" );
document.write( "      y > 0\r\n" );
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document.write( ">>...get 400,000 for each sirplane sold...<<\r\n" );
document.write( ">>...Cost to make airplane - 60,000...<<\r\n" );
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document.write( "So the profit made on an airplane is \r\n" );
document.write( "400000 - 60000 = 340000\r\n" );
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document.write( "So the profit made on x airplanes is 340000x\r\n" );
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document.write( ">>...850,000 for each helicopter sold...<<\r\n" );
document.write( ">>...Cost to make helicopter - 90,000...<<\r\n" );
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document.write( "So the profit made on a helicopter is \r\n" );
document.write( "850000 - 90000 = 760000\r\n" );
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document.write( "So the profit made on y helicopters is 760000x\r\n" );
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document.write( "So the total profit P for making x airplanes and\r\n" );
document.write( "y helicopters is\r\n" );
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document.write( "P = 340000x + 760000y\r\n" );
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document.write( "So to state the problem correctly:\r\n" );
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document.write( "Maximize the objective function\r\n" );
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document.write( "P = 340000x + 760000y\r\n" );
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document.write( "subject to the constraints:\r\n" );
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document.write( "      x < 50\r\n" );
document.write( "      y < 30\r\n" );
document.write( "2x + 3y < 120\r\n" );
document.write( "      x > 0\r\n" );
document.write( "      y > 0\r\n" );
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document.write( "We draw the graphs of these equations, formed\r\n" );
document.write( "by replacing the symbols of inequality by\r\n" );
document.write( "equal signs:\r\n" );
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document.write( "      x = 50  (a vertical line 50 units right of the y-axis)\r\n" );
document.write( "              (the feasible region is on or left of this line) \r\n" );
document.write( "      y = 30  (a horizontal line 30 units above the x-axis\r\n" );
document.write( "              (the feasible region is on or below this line) \r\n" );
document.write( "2x + 3y = 120 (a slanted line with intercepts (60,0), (0,40)\r\n" );
document.write( "              (the feasible region is on or between this line\r\n" );
document.write( "               and the x- and y- axes.  \r\n" );
document.write( "      x = 0   (the y-axis)\r\n" );
document.write( "              (the feasible region is on or right of the y-axis \r\n" );
document.write( "      y = 0   (the x-axis)\r\n" );
document.write( "              (the feasible region is on or above the x-axis) \r\n" );
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document.write( "The feasible region is this polygon:\r\n" );
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document.write( "Find the corner points by substitution using the \r\n" );
document.write( "equations:\r\n" );
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document.write( "Now substitute each of those corner points in the\r\n" );
document.write( "objective function and you'll find that the optimum\r\n" );
document.write( "point is (15,30) for a profit of $27,900,000 when\r\n" );
document.write( "they make 15 airplanes and 30 helicopters.\r\n" );
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document.write( "Edwin
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