## Using Lagrange multpliers to maximize volume

You've been given $73,000 for materials to design a room in the form of a right pyramid. (i.e. a pyramid with the vertices (0,0,0), (a,0,0), (0,b,0) and (0,0,c) where a b and c are real positive numbers. One wall is made of glass costing$3 per sqft. The rest is to be made of concrete at \$8.50 per square foot.

Use vectors to computer the total surface area of the room in terms of a, b and c. Also, determine the volume of the room in terms of a, b and c.

Also, use lagrange multipliers to set up the problem to be solved that will give the room the largest possible volume.

Thanks for any help in advance