Luigi has utility function U=5XY. His income is 100, the price of X is 5 and the price of Y is 2.
a. What is the budget constraint?
b. What is the Lagrange function?
c. Take the derivatives of the Lagrange and set them equal to zero.
d. What is the demand of X and Y (as a function of Px and Py?) Make sure to show your algebra.