The upscale toy store August Kids has a picture window with 100 linear feet of display space. The theme this month is bicycles and tricycles. At least ten tricycles and eight bicycles are to be displayed. Each tricycle needs three linear feet of space in the window display, and each bicycle requires five linear feet. August Kids makes a profit of $40 on each tricycle and $80 on each bicycle it sells. The probability that, on a given day, a displayed tricycle will be sold is 0.10 and that a displayed bicycle will be sold is 0.12.
The store manager, Bob (high profit) Pusher, is in a contest with other store managers and wants the display arranged to maximize daily profit. The store sales team, Mary (commissions forever) Taylor and Pete (count my sales) Simpson, wants the display arranged to maximize the total expected number of daily sales of tricycles and bicycles. The warehouse manager, Homer Tyler, is interested in keeping his workload down and wants the display arranged to minimize the total number of tricycles and bicycles displayed.
Because Bob, Mary, Pete, and Homer know you understand Linear Programming they have come to you for assistance. You recognize immediately that there is not a single solution that will satisfy all three desires. Using Linear Programming determine the optimal number of tricycles and bicycles that August Kids should display in its picture window for each of the objectives. Present your results in a single report to the three groups - Store manager, Sales team, and Warehouse manager. Do you see, from your analysis any suggested compromise?