Problem 4. A small aerospace company will be introducing a new line of lightweight bicycle frames to benefit from the recent interest in dual use technologies. The frames can be made from special aluminum and composite alloys. The frames will be produced in two models, "Deluxe and Professional. The anticipated profits are currently $10 for a deluxe frame and $16 for a professional frame. The number of pounds of each alloy required for each frame is summarized below: Deluxe Professional Aluminum Alloy 2 4 Composite Alloy 3 2 The supplier can deliver 100 lbs. of the aluminum alloy per week and 80 lbs. of the composite alloy per week. a) What is the optimal weekly production schedule? b) Within what limits must the unit profits lie for each of the frames for the solution to remain optimal? c) Suppose an additional amount of the aluminum alloy were made available for $2.50 per pound. Should it be purchased