document.write( "Question 540293: Can you help me with the constraints on this linear programming question?
\n" ); document.write( "A tourist agency can sell up to 1200 travel packages for a football game. The packages include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight. The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers. The agency can locate no more than 10 planes for the travel packages. Each package with a nonstop flight sells for $1200, and each package with a two-stop flight sells for $900. Assuming each plane will carry the maximum number of passengers, find the maximum revenue for the agency.\r
\n" ); document.write( "\n" ); document.write( "Please and Thank You. \n" ); document.write( "
Algebra.Com's Answer #353671 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A tourist agency can sell up to 1200 travel packages for a football game.
\n" ); document.write( " The packages include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight.
\n" ); document.write( " The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers.
\n" ); document.write( " The agency can locate no more than 10 planes for the travel packages.
\n" ); document.write( " Each package with a nonstop flight sells for $1200, and each package with a two-stop flight sells for $900.
\n" ); document.write( " Assuming each plane will carry the maximum number of passengers, find the maximum revenue for the agency.
\n" ); document.write( ":
\n" ); document.write( "Let x = number of 150 passenger planes
\n" ); document.write( "Let y = number of 100 passenger planes
\n" ); document.write( ":
\n" ); document.write( "Number of airplanes:
\n" ); document.write( "x + y =< 10
\n" ); document.write( "Put in the general (y=) form, to plot on a graph
\n" ); document.write( "y =< 10 - x; (purple line)
\n" ); document.write( ":
\n" ); document.write( "Number of travel packages sold:
\n" ); document.write( "150x + 100y =< 1200
\n" ); document.write( "100y =< 1200 - 150x
\n" ); document.write( "y =< 1200/100 - (150/100)x
\n" ); document.write( "y =< 12 - 1.5x; (green line)
\n" ); document.write( ":
\n" ); document.write( "The graph:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+12%2C+-2%2C+15%2C+10-x%2C+12-1.5x+%29+\"
\n" ); document.write( ":
\n" ); document.write( "Feasibility region is at or below the purple or green lines whichever is lowest
\n" ); document.write( ":
\n" ); document.write( "The vertices:
\n" ); document.write( "x = 8, y = 0
\n" ); document.write( "x = 0, y = 10
\n" ); document.write( "Solve the two equation system to find the other vertici
\n" ); document.write( "150x + 100y = 1200
\n" ); document.write( "Simplify, divide by 100
\n" ); document.write( "1.5x + y = 12
\n" ); document.write( "x + y = 10
\n" ); document.write( "----------------subtract, find x
\n" ); document.write( ".5x = 2
\n" ); document.write( "x = 2/.5
\n" ); document.write( "x = 4
\n" ); document.write( ":
\n" ); document.write( "Find y:
\n" ); document.write( "4 + y = 10
\n" ); document.write( "y = 6
\n" ); document.write( "The 3rd vertici is x = 4, y = 6, 4 ea 150 pass planes, 6 ea 100 pass planes
\n" ); document.write( ":
\n" ); document.write( "Revenue:
\n" ); document.write( "4*150*1200 = $720,000
\n" ); document.write( "6*100*900 = $540,000
\n" ); document.write( "--------------------
\n" ); document.write( "total is $1,260,000 for 4 ea 150 pass planes and 6 ea 100 pass planes
\n" ); document.write( "But
\n" ); document.write( "Max revenue would be 8 full 150 pass planes, forget the 100 pass planes
\n" ); document.write( "8 * 150 * 1200 = $1,440,000\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "
\n" );