After the initial market research, Sam decided to offer $2$ choices on his menu. They are deep fried chicken breast with sweet chilli sauce and mayonnaise, respectively. Both of them comes with $2$ slices of brown bread. Sam will rent the university onsite kitchen and make the food freshly in his kitchen.

One portion of these deli requires $250$g $(0\mathrm{.}25$kg$)$ of deep$-$fried chicken breast and $2$ slices of brown bread. The sweet chilli option requires $20$g $(0\mathrm{.}02$kg$)$ of sauce. The mayonnaise option requires $30$g $(0\mathrm{.}03$kg$)$ of sauce. It will cost Sam $2$ minutes and $30$ seconds to make $1$ portion of the sweet chilli option and $3$ minutes to make the mayonnaise option.

Every portion of sweet chilli seasoned deli makes $2\mathrm{.}5$ gross profit while every portion of mayonnaise seasoned deli makes $2$ gross profit. Sam wants to make at least $20$ portions of sweet chilli option and at least $80$ portions of mayonnaise option every week.

Every week, Sam plans to work $25$ hours. He wants to order the minimum amount of raw materials from the wholesaler at the beginning of the business. The wholesaler requires the weekly minimum order

Unit: As specified

Deep fried chicken breast kg

Bread $($slices$)$

Sweet chilli sauce kg

Mayonnaise kg

$70$

$560$

$4$

$10$

Sam is able to sell as much as he can produce every week according to the initial market research. Based on the information above, please help Sam to find the optimal production strategy $($i$.$e$.$ the maximum gross profit he could achieve every week.$)$ Use the linear programming $-$ the graphical approach to resolve the question. Marks will be awarded to each step.