C&A Dairy makes $5$ different flavors of ice cream. The machine must be setup properly for making each flavor. Setup time is $45$ minutes and production time is $30$ minutes per gallon for each flavor of ice cream. Demands $($in gallons per hour$)$ for the ice cream follow:

Vanilla Cherry Strawberry Chocolate Mint

$0\mathrm{.}30\mathrm{.}20\mathrm{.}10\mathrm{.}50\mathrm{.}1$

How many gallons of vanilla ice cream should C&A produce in each production cycle to minimize inventory while satisfying demand?