A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: the adult Open Trail, the adult Cityscape, the girl's Sea Sprite, and the boy's Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The LP model should maximize profit. There are several conditions that the store needs to worry about. One of these is space to hold the inventory. The adult bikes need two feet, but each children's bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The children's bikes need 4 hours each; the Open Trail needs 5hours and the Cityscape needs 6 hours. The store would like to place an order for at least 275 bikes.

1. Formulate a model for this problem.
2. Solve your model with any computer package available to you.
3. How many of each kind of bike should be ordered and what will the profit be?
4. What would the profit be if the store had 100 more feet of storage space
5. If the profit on the cityscape increase to $35, will any of the cityscape bikes be ordered
6. Over what range of assembly hour is is the dual price applicable
7. If we required 5 more bikes in inventory, what will happen to the value of optimal solution
8. Which resource should the company work to increase, inventory space assembly line