This Linear Programming problem centers around a start$-$up $($again$,$ your name here$)$ Co$.$ It would be best if you maximized monthly profit by deciding on the production quantities of multiple products. You will analyze constraints related to resources and labor availability, all under budget limitations$.$ Again, we are working within your framework, so make the numbers as simple or as complex as your mind wants. Make sure to give me a feasible solution. Infeasibility isn't good in academia or the real world! Objective Function: Maximize the total monthly profit from producing multiple products $($e$.$g$.,$ Product A and Product B$).$ Each product must yield a different profit margin. Constraints: Resource Constraints: Each product requires two different amounts of the same essential resource $($materials$).$ The company has limited quantities of these resources each month. Labor Hours: You also have a limited number of labor hours each month, and each product requires a different amount of each labor type. Budget Constraints: A maximum spending budget on raw materials or labor. Remember, you live in the real world, so$,$ again, tell me if your market is $($growing$,$ stagnant, or declining$)$ and if the city you are in has a population of $(<50,000,50,000-500,000,+500,000).$ This will tell you how changes in profit margins, resource availability, or market demand might affect the optimal production mix. This determines the "range of optimality" for profits or "what$-$if$"$ analysis. Frame your start$-$up's products in an industry context, such as eco$-$friendly products, technology components, or sustainable goods, to make the problem relatable and highlight how LP can optimize production planning for profitability and efficiency in real business scenarios. Develop an LP Model by applying an objective function and constraint setup to form a complete LP model. Graphical Solution: For this two$-$variable scenario, plot feasible regions and optimal points, which will demonstrate your graphical LP skills. What are the vertices, and what is the optimal solution in your scenario. Sensitivity Analysis Interpretation: To show me how different parameters influence the model outcomes, explain what would happen $($just pick one$)$ if the labor changed $20\%$ up or $20\%$ down.