$(1$ point$)$

A diet is to contain at least $1124$ units of carbohydrates, $1828$ units of proteins, and $2136$ calories. Two foods are available: $F_1$ which costs $$0\mathrm{.}09$ per unit and $F_2,$ which costs $$0\mathrm{.}08$ per unit. A unit of food $F_1$ contains $1$ units of carbohydrates, $2$ units of proteins and $4$ calories. A unit of food $F_2$ contains $9$ units of carbohydrates, $8$ units of proteins and $6$ 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.

Note: You can earn partial credit on this problem.