Greetings - the following is one question broken into three parts - you need one part to answer the other. Thank you for your help!

A rectangular box without a top is to be made from 12 square feet of cardboard. What is the "objective function" (i.e., the thing we're trying to maximize)?

a) V = x²+ y²+ z²b) S = 2xy +2xz +2yz c) S= xy + 2xz + 2yz d) V = xyz

Now, what is the constraint function? a) S = 2xy +2xz +2yz b) S= xy + 2xz + 2yz c) V = xyz d) V = x2+ y2+ z2 Now, use Lagrange multipliers and find the

maximum volume. a) 16 b) 4 c) 8 d) 12