Hello all, I am stuck on a Calc. 3 problem involving maximization. I've got the word problem into equations but I get stuck finding the gradient of the constraint function. We are supposed to be using Lagrange Multipliers to solve.
Problem: The material for constructing the base of an open box costs 1.5 times as much per unit are that of it's sides. For a fixed amount of money C, find the dimensions of the box with the largest volume that can be made.
From that I got:
V(x,y,z) = xyz constrained to: 3xy + 4xz + 4yz = 2C
So V(x,y,z) = yzi + xzj + yzk
But what is the gradient of the constraining function? Any help is appreciated!