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. The store needs to worry about several conditions. 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 bikes need 4 hours of assembly time, the Open Trail needs 5 hours, and the Cityscape needs 6 hours. The store would like to place an order for at least 27 bikes. a Formulate the LP model for this problem. (4 points) (Show all the details of your model. If you do not show the details, you won't get the points.) The LP model for this problem has been solved with a computer package, respond to the following questions (b. to g.) using the computer output provided below. OBJECTIVE FUNCTION VALUE 1) 6850.0000 VARIABLE X1 X2 X3 X4 VALUE 100.000000 0.000000 175.000000 0.000000 REDUCED COST 0.000000 13.000000 0.000000 2.000000 ROW 2) 3) SLACK OR SURPLUS DUAL PRICE 125.000000 0.000000 0.000000 8.000000 0.000000 -10.000000 VARIABLE X1 X2 NO. ITERATIONS 2 RANGES IN WHICH THE BASIS IS UNCHANGED OBJ COEFFICIENT RANGES CURRENT ALLOWABLE ALLOWABLE COEFFICIENT INCREASE DECREASE 30.000000 INFINITY 2500000 25.000000 13.000000 INFINITY 22.000000 2.000000 2.000000 20.000000 2.000000 INFINITY X4 RIGHTHAND SIDE RANGES ALLOWABLE ALLOWABLE CURRENT b. How many of each kind of bike should be ordered, and what will the profit be? (2 points) c. What would the profit be if the store had 100 more feet of storage space? (2 points) d. If the profit on the Cityscape increases to 35, will any of the Cityscape bikes be ordered? (2 points) e. Over what range of assembly hours is the dual price applicable? (1 point) If we require 5 more bikes in inventory, what will happen to the value of the optisnal solution? (2 points) Which resource should the company work to increase, inventory space or assembly time? (2 points)