Multiplex Cinema owns and operates a nationwide chain of movie theatres. The 500 properties in the Multiplex chain vary from lowvolume, small-town, single-screen theatres to high-volume, big-city, multiscreen theatres. Popcorn machines in most of the chain’s theatres need to be replaced. New machines can be rented in three sizes: economy, regular, and super. The annual rental costs and the operating costs vary with the size of the machines. The machine capacities in bags of popcorn (for simplicity assume that only one size is sold) and costs are:

1. Calculate the volume level in bags at which the economy popper and the regular popper would earn the same operating profit (loss).

2. The management can estimate the number of bags to be sold at each of its theatres. Present a decision rule that would enable Multiplex’s management to select the most profitable machine without having to make a separate cost calculation for each theatre. That is, at what anticipated range of unit sales should the economy model be used? The regular model? The super model? 

3. Could the management use the average number of bags sold per seat for the entire chain and the capacity of each theatre to develop this decision rule? Explain your answer.

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Popper Model Regular 50,000 bags 120,000 bags 300,000 bags Economy Super Annual capacity Costs: Annual machine rental $8,000 $11,200 $20,200 Popcorn cost per box 0.14 0.14 0.14 Cost of each box 0.09 0.09 0.09 Other variable costs per box 0.14 0.22 0.05