We want three nonnegative numbers, , whose sum is 30In an archery challenge an arrow is fired from the point (3,4,-1)
and is aimed at the plane such that
Each shot is given a score by taking the point where the arrow hit the plane
and multiplying the three coordinates together.
a) If a player shoots the arrow along a direction of [1,1,1]
determine the score for their shot.
(I have solved this one, the answer being (11)(12)(7)=924) . I agree!
b) Determine the direction that the player should aim in order to maximize their score.
. . and whose product is a maximum.
We can use Lagrange multipliers to maximize: .
. . subject to the constraint: .
Or we can recall that, if a set of numbers has a fixed sum,
. . their product is a maximum when they are equal.
Either way, the archer should aim at