Minimum of a Quadratic Function on a Hyperplane

Calculus Level pending

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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