A diet is to contain at least $911$ units of carbohydrates, $1412$ units of proteins, and $1178$ calories. Two foods are available: F$1$which costs $$0\mathrm{.}06$ per unit and F$2,$ which costs $$0\mathrm{.}05$ per unit. A unit of food F$1$ contains $1$ units of carbohydrates, $2$ units of proteins and $8$ calories. A unit of foodF$2$ contains $9$ units of carbohydrates, $8$ units of proteins and $2$ calories. Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutrition requirements. Corner points of the feasible region: If there is more than one corner point, type the points separated by a Comma, $($i$.$e$.(1,2),(3,4)).$ Minimum cost is: $ when F$1=$ units and F$2=$ units.