please add these changes to the following model: While your model's framework is outlined, we need more clarity on the model. Could you please list the ingredients individually and clearly define them? Additionally, include the right$-$hand side values for elements like budgets and hours to make your model practical with real values, avoiding a conceptual model. Another issue is the connection between the variables in certain constraints $($e$.$g$.,$ #$1,$ #$2)$ and the objective functions is unclear. the Topic:

El Fenix is a well$-$established restaurant chain known for its authentic Mexican cuisine. With $63$ dedicated employees and an impressive annual revenue of $$4\mathrm{.}3$ million, optimizing operational efficiency is crucial for sustained growth and profitability. To achieve this, the management aims to streamline staffing decisions, inventory management, and revenue maximization strategies.

Mathematical Model:

Decision Variables:

Let:

$-$ X$\_$i be the number of hours assigned to employee i per week for regular shifts.

$-$ Y$\_$i be the number of hours assigned to employee i per week for overtime shifts.

$-$ I$\_$j be the quantity of ingredient j to be ordered per month.

$-$ S$\_$k be the selling price of menu item k$.$

Constraints:

Staffing Constraints:

$-$ Total regular hours for all employees: $\_($i$=1)^63$ X$\_$i $<=$ Maximum Regular Hours

$-$ Total overtime hours for all employees: $\_($i$=1)^63$ Y$\_$i $<=$ Maximum Overtime Hours

Inventory Constraints:

$-$ Availability of ingredient j: $\_($k in K$)$ Ingredient Usage$\_\{$kj$\}>=$ I$\_$j where K is the set of menu items using ingredient j$.$

$-$ Budget constraint for ingredient procurement: $\_($j$=1)^$N Price$\_$j $*$ I$\_$j $<=$ Budget

Revenue Constraints:

$-$ Total revenue from menu items: $\_($k in K$)$ S$\_$k $*$ Quantity Sold$\_$k $>=$ Target Revenue

Non$-$Negativity Constraints:

$-$ X$\_$i$,$ Y$\_$i$,$ I$\_$j$,$ S$\_$k $>=0$ for all i$,$ j$,$ k

Objective Function:

Maximize total revenue:

Maximize $\_($k in K$)$ S$\_$k $*$ Quantity Sold$\_$k

This model considers staffing, inventory, and revenue aspects to optimize operational efficiency and financial performance for El Fenix restaurant.