Page 72 - 35Linear Algebra

72 The Simplex Method

Finally Pablo knows that oranges have twice as much sugar as apples and that apples
have 5 grams of sugar each. Too much sugar is unhealthy, so Pablo wants to keep the
children’s sugar intake as low as possible. How many oranges and apples should Pablo
suggest that the school board put on the menu?

This is a rather gnarly word problem. Our first step is to restate it as
mathematics, stripping away all the extraneous information:

Example 35 (Pablo’s problem restated)
Let x be the number of apples and y be the number of oranges. These must obey

x ≥ 5 and y ≥ 7 ,

to fulfill the school board’s politically motivated wishes. The teacher’s and parent’s
fruit requirement means that
x + y ≥ 15 ,
but to keep the canteen tidy
x + y ≤ 25 .

Now let
s = 5x + 10y .

This linear function of (x, y) represents the grams of sugar in x apples and y oranges.
The problem is asking us to minimize s subject to the four linear inequalities listed
above.

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