A warehouse storage company must determine how many storage sheds of each size- large or small- to build in its new 8000 square foot facility to maximize rental income. Each large shed is 150 square feet in size, requires $1 per week in advertising, and rents for $50 per week. Each small shed is 50 square feet in size, requires $1 per week in advertising, and rents for $20 a week. The company has a weekly advertising budget of $100 and estimates that it can rent no more than 40 sheds in any given week. 

1) Formulate the LP problem. Must show work.

2) Provide the graphical solution to this problem following the procedure discussed in class. Must show work.

3) At the optimal solution, which constraint is not binding, what is the value of the slack? Provide an economic interpretation of the slack value. Must show work.

4) Suppose the large size shed can be rented for $60 per week, what is the new object function, and new optimal solution(s)? Must show work.