A social studies test contains geography and history problems. Geography problems are worth 5 points each and history problems are worth 15 points each. You can do a geography problem in 1 minute and a history problem in 5 minutes. You have an hour to take the test and may answer no more than 40 problems. Assuming you answer all the problems attempted correctly, (a) how many of each type of problem must you do to earn the highest score? (b) what would the resulting highest score be?