Write down the equation of a utility function and draw an indifference curve that corresponds to each of the following cases.(a) Carol is always willing to give up 2 pizzas in exchange for 1 additional beer no matter how many pizzas and beers she has in her consumption bundle.(b) Bob always consumes beer and pizza in fixed proportions. Specifically, if Bob has 1 pizza, he consumes precisely 2 beers and additional beers represent no additional utility for Bob. Similarly, if Bob has 2 beers, he consumes precisely 1 pizza and additional pizzas represent no additional utility for Bob. In addition, when Bob has 4 pizzas and 10 beers, his utility is 32.(c) Kathy loves pizza and is neutral toward beer (i. e., she neither likes nor dislikes beer). She derives 4 units of satisfaction from each pizza she consumes.

Employees at a library check out books to patrons. books have an isbn and a name. the library sometimes has multiple copies of the same book. books have one or more authors. a patron is an individual who has an active (non-expired) library card. for each library card, we store the person's first and last names and their address. for each employee, we store their employee id, current salary, first and last name and their address. we also store the employee id of their current manager. each time we check out a book to a patron we need to store the date of the transaction, the employee who checked out the book to the patron, and the library card of the patron. some employees have library cards. if an employee patron turns in a book late, the fine that they pay is a percentage of their salary. some employees are authors who have library cards—they are allowed to check out as many books as they like.

You were able to purchase two tickets to an upcoming concert for $100 apiece when the concert was first announced three months ago. recently, you saw that stubhub was listing similar seats for $225 apiece. what does it cost you to attend the concert?

Slow ride corp. is evaluating a project with the following cash flows: year cash flow 0 –$12,000 1 5,800 2 6,500 3 6,200 4 5,100 5 –4,300 the company uses a 11 percent discount rate and an 8 percent reinvestment rate on all of its projects. calculate the mirr of the project using all three methods using these interest rates.