Problem-1: (10 points) In a hybrid-engine vehicle, energy from battery ("b" in Amperes) and from 95 octane unleaded gasoline ("g" in liters) are used intermittently to maximize the distance to be travelled (mileage) between fill- ups and charge-ups. If mileage (M) in kilometers is found out to be: M=90 b + 100 g - 3b²- 5g² - 2 bg find the values of "b" and "g" that will maximize mileage M, find the maximum mileage and prove that this is a maximum.