Greenleaf Caf $$e needs to plan its weekly production of three types of sandwiches: Avocado Delight, Chicken Caesar, and Veggie Panini. The caf $$e aims to maximize its profit while managing the availability of key ingredients. The key ingredients are bread, lettuce, and chicken. Avocado Delight sells for a profit of $$6$ per sandwich. It requires $2$ slices of bread, $3$ leaves of lettuce, and no chicken. Chicken Caesar sells for a profit of $$8$ per sandwich. It requires $2$ slices of bread, $2$ leaves of lettuce, and $1$ slice of chicken. Veggie Panini sells for a profit of $$9$ per sandwich. It requires $2$ slices of bread and $4$ leaves of lettuce, and no chicken. Greenleaf Caf $$e has a total of $200$ slices of bread, $250$ leaves of lettuce, and $100$ slices of chicken available for the week. Additionally, the caf $$e must produce at least $10$ Avocado Delight sandwiches due to their popularity.

The objective of the Caf $$e is to maximize their profit.

a$.$ Formulate the problem as a linear program.

b$.$ What is the optimal number of each sandwich type? What is the maximum possible profit that Greenleaf Caf $$e can earn? Please, print a copy of the Excel output $($a screenshot of the spread$-$ sheet, the answer report, and the sensitivity report$).$

c$.$ Suppose Greenleaf Caf $$e is given an offer to purchase an additional $20$ slices of chicken at a total cost of $$20.$ Should they accept this offer? Why or why not? If the answer is yes, what will be the new optimal amounts of each sandwich type?

d$.$ Suppose now that the caf $$e is given another offer to purchase an additional $20$ slices of bread at a total cost of $$20.$ Should they accept this offer? Why or why not? If the answer is yes, what will be the new optimal amounts of each sandwich type?