1. In her last-minute preparations for final exams, a student has set aside five hours to split between studying for two subjects, finance and economics. Her goal is to maximize the average grade received in the two courses. (Note that maximizing the average grade and maximizing the sum of the grades are equivalent goals.) According to her best guesses, grades vary with study as follows: Study Hours 0 1 2 3 4 5 Finance Grade 70 78 83 88 90 92 Study Hours Economics Grade 0 1 2 3 4 5 75 81 85 87 89 90 a. List the marginal values of additional hours worked for each subject b. How much time should the student spend studying each subject? c. Suppose the student also is taking an accounting exam and estimates that each hour of studying will raise her grade by three points. She has allotted two hours for studying accounting (in addition to the five hours already mentioned). Is this an optimal decision? Explain. (Assume her objective is to maximize her average grade across the three courses.)

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4. The BestElect electronics store is having a sale on November 8th on any new electronics purchased. Every customer will receive $50 off their purchase of a new electronic item. They are also offering a student discount on every item in the store for the whole month of November. If you can prove you are a student, you will receive 15% off any item. Let x be the price of any new electronic item in the store. a. Write a function P(x) that represents the price of a new electronic item on November 8th for any customer. b. Write a function D(x) that represents the price you will pay for an item after the student discount is applied during any day in November. Now, we have two functions P and D that depend on the price of the item, x. P is a rule that says "take the price of the item, then subtract $50." D is a rule that says "take the price, then take 85% of it." If you want to take advantage of both sales, a composition of functions is necessary! But is there a difference between P(D(x))…

2. A small college is trying to predict enrolment for the next academic year. Thevice president for business states that enrolment has tended to follow apattern described by E = 18,000 – 0.5P, where E denotes total enrolment andP is yearly tuition.a) If the school sets tuition at €20,000, how many students can it expect to enrol?b) If the school wants to maximize total tuition revenue, what tuition should itcharge?c) As the vice president for business, what tuition would you recommend? Explainbriefly.d) Due to a strong post-COVID-19 recovery, the income conditions in the regionimprove substantially. Explain in one sentence how this could affect the college’senrolment pattern and the enrolment level maximizing its tuition revenue.