Cleopatra wants a box made to hold her jewels. It is to be 8 cubic cubits. The bottom is to be made of gold sheet, the four sides to be made of silver sheet, and the top is to be made of pearl- encrusted sheet welded to gold sheet. Gold sheet costs 16 shekels per square cubit, silver sheet costs 6 shekels per square cubit, and pearl-encrusted sheet costs 8 shekels per square cubit. It will need two gold hinges at a cost of 4 shekels each and a gold handle at 5 shekels. Silver to silver welds cost 2 shekels per cubit, silver to gold welds cost 4 shekels per cubit, and pearl sheet to gold sheet welds cost 5 shekels per cubit. a) What is the minimum cost of such a box and what are its dimensions? Use the method of Lagrange Multipliers, and use Wolfram Alpha to solve the system. b) If you normally charge 1 shekel for 4 hours of labor and it takes you 30 hours to make the box, what is the maximum profit (or loss) you would get if Cleopatra offers you 325 shekels for the job