Hello, Jenna!

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