document.write( "Question 1208007: A new ship is being designed to have two types of cabin accommodation for the
\n" ); document.write( " crew. Each type A cabin accommodate 6 passengers and each type B cabin
\n" ); document.write( " accommodate 3 passengers. The maximum number of passengers the ship
\n" ); document.write( " can accommodate is 330. Each type A cabin has 50m2 of space and each type
\n" ); document.write( " B cabin has 10m2 of space. The total amount of cabin space should not exceed
\n" ); document.write( " 2300m2
\n" ); document.write( "i)Write down inequalities to represent this information. (2 Marks)
\n" ); document.write( "ii)Using the graphical method find the number of cabins of each type required to maximize the income given that income from one voyage of type A cabin is kSh 6,000 and that of type B cabins is ksh 1,800. \n" ); document.write( "
Algebra.Com's Answer #846116 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Maximize z = 6000x+1800y\r\n" );
document.write( "\r\n" );
document.write( "subject to constraints\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We find the intercepts and draw the lines 6x+3y=330 and 50x+10y=2300\r\n" );
document.write( "\r\n" );
document.write( "By the inequality symbols, we see the feasible region is on and\r\n" );
document.write( "above the x-axis, on or to the right of the y-axis, and on or below \r\n" );
document.write( "the other two lines.  So we shade the feasible region:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we evaluate the objective function  z = 6000x+1800y\r\n" );
document.write( "at each corner point of the feasible region.\r\n" );
document.write( "\r\n" );
document.write( "At (0,0), 6000(0)+1800(0) = 0 kSh\r\n" );
document.write( "At (46,0), 6000(46)+1800(0) = 276,000 kSh\r\n" );
document.write( "At (40,30), 6000(40)+1800(30) = 494,000 kSh\r\n" );
document.write( "At (0,110), 6000(0)+1800(110) = 198,000 kSh\r\n" );
document.write( "\r\n" );
document.write( "So the maximum profit is 494,000 kSh when there are 40 type A\r\n" );
document.write( "cabins and 30 type B cabins.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );