NPV and IRR
NPV and IRR can be calculated from the information given for each case study: you are given initial outlay and future savings. You may assume savings are at perpetuity if no information on the savings life time is given. How you choose the discount rate should be carefully explained.
TR and TC can be theoretical functions used to compute profits. If you have some information on costs and revenue from annual reports, for example, you can take those into account when specifying the TR and TC functions. You should list carefully the assumptions you are making when specifying those functions. Once you have a profit function you find the value of output which maximizes profits before and after the introduction of the program. Profit maximizing outputs will be functions of the (unknown) parameters of the theoretical TR and TC functions.
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