Based on Enclosure A and Enclosure B$,$ we would like to know the optimal production quantity for each product $($SC$-$A$,$ SC$-$B$,$ SC$-$C$,$ SC$-$D$,$ S$-10,$ S$-20,$ S$-30,$ S$-40).$ The goal is to maximize the total profit. We would also like to do the sensitivity analysis. First, formulate the problem as a linear programming formulation. Then, solve the problem using Excel and answer the following questions.

Hint: In this linear programming formulation, we have $8$ variables $($the quantities of SC$-$A$,$ SC$-$B$,$ SC$-$C$,$ SC$-$D$,$ S$-10,$ S$-20,$ S$-30,$ S$-40)$ and $7$ constraints $($for the usage of wood, trim, granite, solid surface, laminate, assembly labor, and finish labor$)$ plus the non$-$negatively constraint. This formulation is similar to tutorial question Q$1$ where we have $3$ variables $($quantities of products A$,$ B$,$ and C$)$ and $3$ constraints $($for the usage of milling time, inspection time, and drilling time$).$