SOLUTION: A new ship is being designed to have two types of cabin accommodation for the crew. Each type A cabin accommodate 6 passengers and each type B cabin accommodate 3 passeng

Question 1208007: A new ship is being designed to have two types of cabin accommodation for the
crew. Each type A cabin accommodate 6 passengers and each type B cabin
accommodate 3 passengers. The maximum number of passengers the ship
can accommodate is 330. Each type A cabin has 50m2 of space and each type
B cabin has 10m2 of space. The total amount of cabin space should not exceed
2300m2
i)Write down inequalities to represent this information. (2 Marks)
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.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

Maximize z = 6000x+1800y

subject to constraints



We find the intercepts and draw the lines 6x+3y=330 and 50x+10y=2300

By the inequality symbols, we see the feasible region is on and
above the x-axis, on or to the right of the y-axis, and on or below 
the other two lines.  So we shade the feasible region:



So we evaluate the objective function  z = 6000x+1800y
at each corner point of the feasible region.

At (0,0), 6000(0)+1800(0) = 0 kSh
At (46,0), 6000(46)+1800(0) = 276,000 kSh
At (40,30), 6000(40)+1800(30) = 494,000 kSh
At (0,110), 6000(0)+1800(110) = 198,000 kSh

So the maximum profit is 494,000 kSh when there are 40 type A
cabins and 30 type B cabins.

Edwin

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