5. (4 marks) Ann and Bruce share an apartment. The landlord pays for heat and air conditioning. Ann and Bruce both play chess, and they own a chess set. Let T be the temperature in the apartment in degrees Celsius and G be the number of games of chess they play against each other each week. Assume T and G are continuously variable, and Ann's utility function is

UA(T, G) = ?(T ? 20)^2 ? (G ? 4)^2 ,

and Bruce's utility function is

UB(T, G) = ?(T ? 24)^2 ? (G ? 2)^2 .

5. (4 marks) Ann and Bruce share an apartment. The landlord pays for heat and air conditioning. Ann and Bruce both play chess, and they own a chess set. Let T be the temperature in the apartment in degrees Celsius and G be the number of games of chess they play against each other each week. Assume T and G are continuously variable, and Ann's utility function is UA(T, G) = -(T -20)2 - (G -4)2, and Bruce's utility function is UB(T, G) = -(T - 24)2 - (G -2)2. As precisely as you can, describe the Pareto efficient values for T and G