6. [24 points] Obviously, Lagrange multipliers can be used to optimize lasagna. You have $108 to spend on ingredients. It's the good stuff. Pasta costs $4 a box, Sauce is $9 a jar, and Cheese is $16 per pound. (This cheese is amazing.) Let x be the number of boxes of pasta, y be the number of jars of sauce, and z be the number of pounds of cheese. Your lasagna will be most awesome when the ingredients are in harmony, that is, when the sum of the reciprocals, ++, is minimized. Trust me on this. Using Lagrange multipliers, find the quantities of each ingredient that maximize awesomeness. I