# Linear Programming : Corner Point Method

Dr Wu can cure colds with his 3 layer pills. They come in two sizes, regular and king size. Regular size contains 2 grains of aspirin, 5 grains of bicarbonate, and 1 grain of codeine. For king size, it is 1 grain of aspirin, 8 grains of bicarbonate, and 6 grains of codeine. Dr Wu shows that is requires at least 12 grains of aspirin, 74 grains of bicarbonate and 28 grains of codeine to affect his cure. Determine the least number of regular and king size pills he should prescribe to meet those requirements.

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#### Solution Preview

number of regular size = x

number of King size = y

Aspirin

2x + 1y >= 12 ..(1)

Bicarbonate:

5x + 8y >= 74 ..(2)

Codeine:

1x + 6y >= 28 ...(3)

number of pills:

z = x+y => ...

#### Solution Summary

A problem is solved bthrough linear programming. Constraints are set up and a maximum value is obtained.