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, multi-screen theaters. The management is considering installing machines that will make popcorn on the premises. These machines would allow the theaters to sell popcorn that would be freshly popped daily rather than the pre-popped corn that is currently purchased in large bags. This proposed feature would be properly advertised and is intended to increase patronage at the company's theaters.

The machines can be purchased in several different sizes. The annual rental costs and the operating costs vary with the size of the machines. The machine capacities and costs are shown below.

{Required:}

(a) Calculate the volume level in boxes at which the Economy Popper and Regular Popper would earn the same profit (loss).

(b) The 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 the 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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Popper Model Economy Regular Super Annual capacity............... Costs: 50,000 boxes 120,000 boxes 300,000 boxes Annual machine rental...... $8,000 $11,000 $20,000 Popcorn cost per box........... .13 .13 .13 Other costs per box............. .22 .14 .05 Cost of each box............ .08 .08 .08