The owner of the theater would like to experiment with segmenting the market into people who have

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Question:

The owner of the theater would like to experiment with segmenting the market into people who have a willingness $-$ to $-$ pay $>$ $ $25$ and those who have a willingness $-$ to $-$ pay less than or equal to $ $25 .$ The owner still pays $ $15$ in royalties per person who views the film. The owner would like to find answers to the following questions, but the demand must be an integer value.

a $.$ Find the price per ticket for the two market segments that maximize contribution. How many people would the owner of the theater have in each of the segments? How much will the theater owner make?

b $.$ With segmentation, the theater owner should increase her profit. If the segmentation is fair the consumers should also increase their benefit $($ surplus $) .$ Find the consumer benefit $($ surplus $) .$

c $.$ Find the prices that maximize contribution if the cannibalization rate is $10$ percent.

d $.$ Find the optimal segmentation level that maximizes contribution without cannibalization.

e $.$ Find the optimal segmentation level that maximizes contribution with cannibalization of $10 % .$

f $.$ With the market segmented at $ $25,$ find the maximum cannibalization rate that the theater owner can afford?

g $.$ If the theater only has a capacity of $2500$ seats, how much would the theater owner be willing to pay to eliminate that constraint? Do not segment the market.