William Company owns and operates a nationwide chain of movie theaters. The 500 properties in the William chain vary from low-volume, small-town, single-screen theaters to high-volume, big-city, multiscreen theaters.
The management is considering installing machines that will make popcorn on the premises. These machines would allow the theaters to sell freshly popped popcorn rather than prepopped corn that is currently purchased in large bags. This new feature would be advertised and is intended to increase patronage at the company’s theaters.
Annual rental costs and operating costs vary with the size of the machines. The machine capacities and costs are as follows:
| Economy | Regular | Super | |
| Annual capacity (boxes) Costs | 50,000 | 120,000 | 300,000 |
| Annual machine rental | $8,000 | $11,000 | $20,000 |
| Popcorn cost per box | 130 | 130 | 130 |
| Other costs per box | 220 | 140 | 050 |
| Cost of each box | 080 | 080 | 080 |
Required:
a. Calculate the volume level in boxes at which the economy popper and regular popper would earn the same profit (loss).
b. Management can estimate the number of boxes to be sold at each of its theaters. Present a decision rule that would enable William’s management to select the most profitable machine without having to make a separate cost calculation for each theater.
c. Could management use the average number of boxes sold per seat for the entire chain and the capacity of each theater to develop this decision rule? Explain your answer.
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