John purchased three bonds to form a portfolio as follows: Bond A has semi-annual coupons at 4%, a duration of 21.46 years, and was purchased for 980. Bond B is a 15-year bond with a duration of 12.35 years and was purchased for 1,015. Bond C has a duration of 16.67 years and was purchased for 1,000. Calculate the duration of the portfolio at the time of purchase.

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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.

Match each item to check for while reconciling a bank account with the document to which it relates. (there's not just one answer) 1. balancing account statement 2. balancing check register a. nsf fees b. deposits in transit c. interest earned d. bank errors