# Minimum of a Quadratic Function on a Hyperplane

Calculus Level 5

Consider the minimum of

$F = \sum_{i=1}^{10} { a_i x_i^2 }$

subject to

$\sum_{i=1}^{10} { b_i x_i } = c$

with $$a_i = i$$ and $$b_i = i$$ and $$c = 10$$

If the minimum is $$F^*$$ , find $$100 / F^*$$

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