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 40, 28, 25, and 21. 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. An adult's bike needs two feet, but a child's bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The child's bike need 4 hours of assembly time; the Open Trail needs 5 hours and the Cityscape needs 7 hours. The store would like to place an order for at least 275 bikes.

a. Formulate a linear programming model, assume X1=the number of the adult Open Train bike ordered X2=the number of the adult Cityscape bike ordered X3=the number of the girls Sea Sprite bike ordered X4=the number of the boys Trail Blazer bike ordered

b. Solve your linear programming model in part a, using EXCEL Solver, and interpret the results. In other words, how many of each kind of bike should be ordered and what will be the maximum profit? Explain using at least 70 words.

c. What would be the optimal (maximum) profit be if the store had 120 more feet of storage space? Explain using at least 70 words. Justify your answer based on your sensitivity report.

d. Which resource should the company work ton increase, inventory space or assembly time? Explain using at least 70 words. Justify your answer based on your sensitivity report.