Rangan runs a snack cart that serves two types of snacks idli and dosa. One plate of idli uses 5 oz batter and one plate of dosa uses 2 oz batter. Today he expects to serve between 12 and 15 total plates of idli and dosa and so he has prepared 40 oz of batter. He aims to use up all the batter otherwise it will go bad, but, he can make more batter if needed. It takes 5 min to cook a plate of dosa and 20 min to cook a plate of idli, he can cook only one item at a time. Rangan is short on oil for his stove so he would like to minimize its run time. Required:
a. How many plates of each snack can he deliver, what is the stove run time?
b. Will he use up all his batter, or, how much additional batter will he have to make?