Question

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?"

Answer 1

Solution:

1. The arcade is open for 100 hours per week

Video game:

Revenue = $20/hour

Occupancy Rate = 40%

Maintenance cost = $100 / machine / week

Maximum no of machines that can be installed = 5

Space needed for installing one machine = 50 square feet

Contribution margin = Sales – variable cost

Total occupancy hour = 100 * 40/100

                                                = 40 hours

Revenue = 40 * $20 = $800 / machine

Maintenance cost = $ 100 / machine

Contribution margin = $800 - $100

                                                = $ 700

Profitability = $ 700 / 50 ft²

                = $14 / square feet

Dance game:

Revenue = $40/hour

Occupancy Rate = 30%

Maintenance cost = $300 / machine / week

Maximum no of machines that can be installed = 2

Space needed for installing one machine = 75 square feet

Contribution margin = Sales – variable cost

Total occupancy hour = 100 * 30/100

                                                = 30 hours

Revenue = 30 * $40 = $1200 / machine

Maintenance cost = $ 300 / machine

Contribution margin = $1200 - $300

                                                = $ 900

Profitability = $ 900 / 75 ft²

                = $12 / square feet

Simple games:

Revenue = $15/hour

Occupancy Rate = 10%

Maintenance cost = $0 / machine / week

Maximum no of machines that can be installed = 6

Space needed for installing one machine = 10 square feet

Contribution margin = Sales – variable cost

Total occupancy hour = 100 * 10/100

                                                = 10 hours

Revenue = 10 * $15 = $150 / machine

Maintenance cost = $ 0 / machine

Contribution margin = $150 - $0

                                                = $ 150

Profitability = $ 150 / 10 ft²

                = $15 / square feet

Ranking of the games as per their profitability,

1. Simple games
2. Video games
3. Dance games

Allocating the space based on the profitability,

Simple games = 6*10 square feet = 60 square feet

Video games = 4*50 square feet = 200 square feet

Crash’s expected profit with this allocation:

Simple games

Revenue = no. of machines * Total occupancy hour * revenue per hour

                = 6*10*15 = $900

Maintenance cost = no. of machines * cost

                = 6*0 = $0

Profit = revenue – maintenance cost

                = $900 - $0 = $900

Video games:

Revenue = no. of machines * Total occupancy hour * revenue per hour

                = 4*40*20 = $3,200

Maintenance cost = no. of machines * cost

                = 4*100 = $400

Profit = revenue – maintenance cost

                = $3,200 - $400 = $2,800

Total profit for this type of allocation is $900 + $2,800 = $3,700

b. As per the ranking of profitability the machines should be installed in the order starting with simple game followed by video games and dance games. The remaining space available is 40 square feet will be empty because video games need 50 square feet. Dance game also can’t be installed in this space as it needs 75 square feet.

c. Suggestion:

Install the following machines

Simple games = 6 nos. = 60 square feet

Video games = 3 nos. = 150 square feet

Dance games = 1 nos. = 75 square feet

Total space occupied = 285 square feet

Simple games:

Revenue = no. of machines * Total occupancy hour * revenue per hour

                = 6*10*15 = $900

Maintenance cost = no. of machines * cost

                = 6*0 = $0

Profit = revenue – maintenance cost

                = $900 - $0 = $900

Video games:

Revenue = no. of machines * Total occupancy hour * revenue per hour

                = 3*40*20 = $2,400

Maintenance cost = no. of machines * cost

                = 3*100 = $300

Profit = revenue – maintenance cost

                = $2,400 - $300 = $2,100

Dance games:

Revenue = no. of machines * Total occupancy hour * revenue per hour

                = 1*30*40 = $1,200

Maintenance cost = no. of machines * cost

                = 1*300 = $300

Profit = revenue – maintenance cost

                = $1,200 - $300 = $900

Total profit = $900 + $2,100 + $900

                = $3,900