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:U(R, S) = R S

so that her MRS is given by: MRS = S / R = (U/R) / (U/S) = S/ R

Let the price of both R and S be fixed at 1.

a.)Write Mary's budget constraint as a function of P_R, P_S,and her construction budget I.

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