In considering medical insurance for a certain operation, let X be the amount (in $) paid for the doctor and let Y be the amount (in $) paid to the hospital. In the past, the variances have been Var(X) = 8,100, Var(Y) = 10,000, and Var(X + Y) = 20,000. Due to increased expenses, it was decided to increase the doctor's fee by $500 and increase the hospital charge Y by 8%. Calculate the variance of the new total claim, i.e. the variance of X + 500 + 1.08Y. (Hint: In this problem, you cannot simply assume independence of X and Y. Start by finding the covariance between X and Y from the information provided about the past variances.