American Red Cross Emergency Kits

The international red cross is making plans to airlift emergency food and medical supplies into a large South American city which has recently suffered from extensive flooding. Four items will be air lifted in containers to aid in the recovery from flooding. The four items and their respective volumes per container are shown in the table. The first plane to be sent into the area that has the volume capacity 6000 cubic feet. Determine an equation whose solution set contain all possible combinations of the four items which will fill the plane to its volume capacity.

Items cubic feet,: Volume per container
Blood: 20
Medical supply kits: 30
Food: 8
water: 6

In a realistic sense what are maximum and minimum possible quantities of each item.
I am able to the first part: 20x+30y+8z+6h=6000, where x=blood.y=medical supplies, z=food and h= water
can any one help me how to maximize or minimize this equation.

Since we don't know the inside dimensions of the cargo hold of the plane or the dimensions of the containers of each kind that are to be loaded, there is not sufficient information to accurately calculate the maximum numbers. However, if we assume the containers just fit without any wasted space, and since there is no constraint given that states we must include at least 1 unit of all 4 supplies, then we can compute the maxima as follows:

20x+30y+8z+6h=6000

x = 300, when y = z = h = 0
y = 200, when x = z = h = 0
z = 750, when x = y = h = 0
h = 1000, when x = y = z = 0

If there must be at least 1 unit of each, then these numbers become

x = 297, when y = z = h = 1
y = 198, when x = z = h = 1
z = 743, when x = y = h = 1
h = 990, when x = y = z = 1

If we want to maximize any particular variable x,y,z,h, then first we must fix the other 3 or provide a sufficient set of constraints that has this effect. For instance, if the requirement is that equal numbers of each supply be included then 90 containers of each supply can fit into the plane.

2009-08-19 12:57:32 by sz

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