Tuesday, September 08, 2009

Blood and Bags

A medical helicopter has a special compartment for carrying blood bags; in particular, the compartment can carry 4 blood bags of any capacity.

Now, the maximum amount of blood needed for any heli-rescue mission is 4.95 units; any more and the patient is already beyond the capabilities of the medical crew. Considering this, it is wise for the helicopter to carry not more than 4.95 units of blood.

Another problem faced is blood wastage. Since blood transfusions involve connecting the blood bag to the patient, the blood in each used bag is 'contaminated' and cannot be reused for other transfusions. Hence, using a 4.95 unit bag for an patient that requires only 0.50 units of blood is discouraged, since 4.45 units of blood are not used and wasted. However, unopened bags can be reused for subsequent missions and are hence not wasted.

Considering the above, it is desired to choose some capacity for each of the 4 blood bags such that the amount of blood wastage in the worst case is minimized. It is assumed that the flight doctor is capable of accurately determining the exact amount of blood needed for transfusion before the transfusion takes place.

What are the capacities of the 4 blood bags?

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