SOLUTION: Find two numbers whose sum is 60, such that the sum of the square of one number plus twelve times the other number is a minimum.

Question 329197: Find two numbers whose sum is 60, such that the sum of the square of one number plus twelve times the other number is a minimum.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.
You are trying to minimize the value of
2.
From eq. 1,

Substitute into eq. 2,

Complete the square to put the equation in vertex form,
Since the coefficient of is positive, the vertex y value(k) will be the minimum.

.
.
.
and would provide the minimum value of 684.

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