SOLUTION: Please help me solve this word problem: Find two positive numbers where the sum of the first and three times the second is 42 such that the product is a minimum.

Question 362402: Please help me solve this word problem:
Find two positive numbers where the sum of the first and three times the second is 42 such that the product is a minimum.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
P = xy, if x + 3y = 42.
From the given, x = 42-3y. Substitute into P = xy:
P = (42 - 3y)y, or
.
This is a quadratic equation whose graph is a parabola facing downward, hence it has a MAXIMUM. The roots are 0 and 14. The maximum happens when y = 7, the average of the two roots. Therefore x = 21. The 1st number is 21, and the 2nd, 7.
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