Mary Day is a university chancellor deciding how to allocate the budget for new buildings. Her preferences over research space (R) and sports facilities (S), both measured in 1,000 sq. ft., are given by

so that her MRS is given by

U(R, S) = R S

MRS = S = U/R = S R U/S R

Let the price of both R and S be fixed at 1. (a) Write Mary's budget constraint as a function of PR, PS, and her construction budget I.

(b) Solve for Mary's optimal bundle (R,S). (Hint: You can set MRS = MRT.)