6.66 Allocating a scarce resource (L04). "Crash" Johnson manages the 1,500-square-foot video arcade and game center at a popular mall. Seeking to renovate and upgrade the arcade, Crash recently removed some old games, freeing up 300 square feet of space. Crash has narrowed his options for new games to the following: Install video games that simulate high-adrenaline activities such as driving a motor- cycle and skiing. Each of these machines would consume 50 square feet of space and generate revenues of $20 per fully occupied hour. Based on the expected 40% occupancy rate, each installed machine would generate maintenance costs of $100 per week. Crash believes that, at a maximum, he could install up to five such machines. Install a dance game. This game allows one or two players to "dance" on pads to match the moves displayed on the screen. Because good players attract considerable numbers of bystanders, Crash budgets 75 square feet per game. While most arcades have at least one such game, Crash does not wish to have more than two games. (He does not currently have the game available.) The dance game generates $40 in rev- enue per occupied hour. With estimated usage at 30%, Crash projects maintenance expenses of $300 per week per machine. Install simple games (e.g., "Whack-a-Mole") aimed at pre-teens and children. These games occupy 10 square feet each and require virtually no maintenance (for all practi- cal purposes, assume it is $0 per week). To maintain balance in his arcade, Crash believes that he could install a maximum of six simple games. Finally, while the simple games generate $15 in revenue per hour occupied, the occupancy rate hovers around 10%. Crash believes that he could deploy any combination of these three options and still maintain the overall balance of games in his video arcade. Required: a. Determine the contribution margin per week per square foot devoted to each kind of game. Based solely on the ranking of the games as per their profitability, allocate the 300 feet in available space to maximize Crash's expected profit per week. What is Crash's expected profit with this allocation? Assume that the arcade is open for 100 hours per week. b. Explain why your solution in part (a) may not fully use all available capacity. c. Suggest an alternative configuration that might help Crash improve his expected profit per week. d. What do you conclude about the validity of the rule "allocate scare capacity among uses to maximize the contribution margin per unit of the scarce resource