Suppose there are two firms (1 and 2) located along a surface water resource and that the profit functions of each firm are provided below, where 7iNSYsLDJFEN13ZU0zrrDQ8e1tBLr7r8ElF is the quantity of water used by firm i.
Firm a:wPHcbYArNlLhwBJRU5ErkJggg==

Firm b: O4fW7gxNIFgBJRU5ErkJggg==

If each firm uses the amount of water that maximizes its own profits, what is the total quantity of water that will be used?
Suppose that there are only 20 total units of water available. What is the allocation of the 20 units of water across the two firms that maximizes total profits?
Relative to the allocation of water that you found in part (b), by how much do total profits decrease if the 20 units are instead evenly distributed to the two firms (in other words, each firm is allocated 10 units of water)?

Salt corporation's contribution margin ratio is 78% and its fixed monthly expenses are $30,000. assume that the company's sales for may are expected to be $89,000. required: estimate the company's net operating income for may, assuming that the fixed monthly expenses do not change.

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.

Bernard made a gift of $500,000 to his brother in 2014. due to bernard’s prior taxable gifts he paid $200,000 of gift tax. when bernard died in 2019, the applicable gift tax credit had increased. at bernard’s death, what amount related to the $500,000 gift to his brother is included in his gross estate?