Cully Furniture buys two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $250 and requires 80 cubic feet of storage space. The company has $80,000 to invest in shelves this week, and the warehouse has 30,000 cubic feet available for storage. Profit for each king bed is $400 and for each queen bed is $200.

1). (10') Please set up the LP model for the above situation.

2). (20') How many king beds (K) and how many queen bed (Q) should be purchased at optimal?

3). (10') Whether we have slack or surplus variable applicable in this question? If we do, what is the value of slack (or/and surplus) variable? What is the meaning behind it?

4). (10') If the furniture company purchases no king beds and 300 queen beds, which resources will be completely used (at capacity)?