Classi Furniture Company (CFC) produces three types of sofas: luxury, classic, sport. They also produce two types of chairs: bergre and dining chairs. Due to the capacity limit, CFC can produce at most 1,5 million products per year. Sofas are produced in facility A with a capacity of 1 million units and the chairs are produced in facility B with a capacity of 750,000 units. CFCs management team requires that classic sofas and sport sofas must constitute at least half of the product mix for the three types of sofas. Also, management wants to have at least 40% of total products are chairs. Profit margins and maximum market demand potentials are given as follows:

Product Type	Capacity Limits (units in 000)	Profit Margin ($/unit)	Maximum Market Potential (units in 000)
Luxury Sofa	1,000	28	400
Classic Sofa	27	370
Sport Sofa	25	130
Bergere Chair	750	22	250
Dining Chair	21	350

1. Write down the mathematical model formulation of optimization problem if CFC wants to maximize its annual profit. Please clearly define the decision variables, express the objective as a function, and show all necessary constraints. (5 points)

1. What is the optimal value of the objective function and decision variables. (3 points)

1. What is the marginal value (shadow price) of an additional 1,000 units of total production capacity? Show your calculations on your Excel sheet. (2 points)

1. What is the marginal value (shadow price) of an additional 1,000 units of facility A? (2 points)