Question

# Ms. Darla White is considering taking a field trip with her 4^{th} grade Enrichment students. Part of the

field trip experience involves riding a bus and stopping by a local deli for lunch. Ms. Brown has more students interested in the trip then she can likely handle ... she is constrained by a number of factors.

First, she must bring adults from the PTA with her on the trip for 'safety' reasons. For now, let's say she is required to have at least 4 adults. She can have more.

**Second, she has a limit to how many people can comfortably fit on the old yellow school bus. Up to 42 students can fit on the school bus, but then there would be no room for any adults. Based on 'average butt size", an adult takes up 1.25 seats as compared to a student. (So, 4 adults take up the space of 5 students). The bus does not have to be totally full. So - consider it to have a capacity of 42 student butts, and that an adult takes up 1.25 units. **

Third, Ms. White can spend at most $180 in lunches. The adult lunches cost $6 apiece, the students, $4 apiece.

a) If Ms. White's goal is to maximize the number of students that go on the field trip, what is the optimal number of adults and students she can bring?

b) Consider a different goal: Ms. White knows that she can gain favor from the parents if she gives them some priority in making this decision of how many students and adults to bring on the field trip. Let's say that the **"Priority Function" is (1.4*Adults + 1.0* Students).** Given the same three requirements stated above, what is the (new, different) optimal number of adults and students that she should bring on the field trip?

I don't understand part b but my teacher has informed us the answer is A=12, S=27, objective function value =43.8

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