Christian Taylor manages a 1,500 square foot video game arcade at the Lakeside Mall. Mr. Taylor wants to freshen up the space and so will be removing some unpopular games, thus freeing up 300 square feet of space. He has several options from which to choose:

1. Install high adrenaline games such as race car driving or skiing. Each one of these machines would take up 50 square feet and generate revenues of $20 per fully occupied hour. Over the course of a day, each installed machine would have a 40% occupancy rate. Based on that expected rate, the weekly maintenance costs would run about $100. At a maximum, Mr Taylor thinks he could install up to five such machines.

2. Install a dance game. This game allows one or two players to dance on pads to match the moves displayed on the screen. Because these games attract a crowd of onlookers, Mr. Taylor would budget 75 square feet per dance game. He Even though most arcades have these games, there is not one currently in the arcade. He does not want to have more than two of these games. The dance game generates $40 in revenue per occupied hour. With average usage at 30%, he projects maintenance expenses of $300 per week per machine.

3. Install simple games (e.g., Whack-a-Mole) aimed at children and pre-teens. These games occupy 10 square feet a piece and virtually no maintenance (so assume the costs are zero per week). To maintain balance in the arcade, Mr. Taylor does not more than six of these games in the arcade. Simple games generate $15 per occupied hour, but the occupancy rate hovers around 10%.

4-1. 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 square feet available to maximize the arcades expected profit per week. Assuming the arcade is open 100 hours per week, what is that expected profit?

4-2. Explain why your solution in 4-1 may not fully use the all available capacity.

4-3. So what is the optimal combination of these three options, while maintaining the overall balance of games in the arcade?

4-4. Comment on your results in relation to the rule allocate scarce capacity among uses to maximize contribution margin per unit of scarce resource.