b) 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. There are several conditions that the store needs to worry about, which are given below. Open Trail (OT) Cityscape (CS) Sea Sprite (SS) Trail Blazer (TB) Requirements Available Space (feet) 2 2 1 1 500 5 6 4 4 1200 Assembly time (hrs) Also, the store would like to place an order for at least 275 total bikes. Formulate LP model which should maximize profit. DO NOT ATTEMPT TO SOLVE. (3 marks) The Management Scientist Output of above LP is given below. OPTIMAL SOLUTION Objective Function Value = 6850.000 Variable Value Reduced Cost 100.000 0.000 CS 0.000 13.000 SS 175.000 0.000 TB 0.000 2.000 Constraint Slack/Surplus Dual Price Space 125.000 0.000 Assembly Time 0.000 8.000 Mang. Reqt. 0.000 -10.000 OT OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value OT 27.500 30.000 CS No Lower Limit 25.000 SS 20.000 22.000 TB No Lower Limit 20.000 Upper Limit No Upper Limit 38.000 24.000 22.000 RIGHT HAND SIDE RANGES Constraint Space Assembly Time Mang. Regt. Lower Limit 375.000 1100.000 250.000 Current Value 500.000 1200.000 275.000 Upper Limit No Upper Limit 1325.000 310.000 1) What would the profit be if the store had 100 more feet of storage space? (2 marks) ii) If the profit on the Cityscape increases to 35, will any of the Cityscape bikes be ordered? (2 marks) If we require 5 more bikes in inventory, what will happen to the value of the optimal solution? aadal