He function $f$ satisfies\[f(x) + f(2x + y) + 5xy = f(3x - y) + 2x^2 + 1\]for all real numbers $x$, $y$. determine the value of $f(10)$.

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

Select the correct answer. sarah works in a coffee house where she is responsible for keying in customer orders. a customer orders snacks and coffee, but later, cancels th snacks, saying she wants only coffee. at the end of the day, sarah finds that there is a mismatch in the snack items ordered. which term suggest data has been violated? a. security b. integrity c. adding d. reliability e. reporting

Abank provides its customers mobile applications that significantly simplify traditional banking activities. for example, a customer can use a smartphone to take a picture of a check and electronically deposit into an account. this unique service demonstrates the bank’s desire to practice which one of porter’s strategies?