A simple optimal portfolio problem is the cash matching problem. Suppose you are given a sequence of future monetary obligations, in dollars, required to be paid at the end of each year over the next 10 years as follows:
YEAR 1 2 3 4 5 6 7 8 9 10
OBLIGATION 100 200 300 400 500 600 700 800 900 1000
We wish to invest now so that these obligations can be met as they occur, accordingly, we must purchase bonds of various maturities and use the associated future cash flows to meet the obligations.
Suppose there are 10 zero coupon bonds available to be purchased, each with a face value of $100. The maturities of the zero coupon bonds span 1 to 10 years, and the price of each zero coupon bond is consistent with a flat term structure: all spot rates are equal to 5% annually. To be clear, we have available a 1-year zero coupon bond with 5% yield, a 2-year zero coupon bond with 5% yield, a 3-year zero coupon bond with a 5% yield, all the way up to a 10-year zero coupon bond with a 5% yield, for a total of 10 zero coupon bonds. The objective function to be minimized is the total cost of the portfolio, which is equal to the sum of the prices of the bonds times the number of units purchased.
How many units of the 5-year zero coupon bond should be purchased in the optimal portfolio? Please round your numerical answer to the nearest integer number of units.

Journalize the following transactions that occurred in september 2015 for aquamarines. no explanations are needed. identify each accounts payable and accounts receivable with the vendor or customer name. sep. 3 purchased merchandise inventory on account from shallin wholesalers, $5,000. terms 1/15, n/eom, fob shipping point. 4 paid freight bill of $80 on september 3 purchase. 4 purchased merchandise inventory for cash of $1,700. 6 returned $500 of inventory from september 3 purchase. 8 sold merchandise inventory to hermosa company, $6,000, on account. terms 2/15, n/35. cost of goods, $2,640. 9 purchased merchandise inventory on account from thomas wholesalers, $8,000. terms 2/10, n/30, fob destination. 10 made payment to shallin wholesalers for goods purchased on september 3, less return and discount. 12 received payment from hermosa company, less discount. 13 after negotiations, received a $200 allowance from thomas wholesalers. 15 sold merchandise inventory to jordan company, $2,500, on account. terms 1/10, n/eom. cost of goods, $1,050. 22 made payment, less allowance, to thomas wholesalers for goods purchased on september 9. 23 jordan company returned $400 of the merchandise sold on september 15. cost of goods, $160. 25 sold merchandise inventory to smithsons for $1,100 on account that cost $400. terms of 2/10, n/30 were offered, fob shipping point. as a courtesy to smithsons, $75 of freight was added to the invoice for which cash was paid by aquamarines. 26 after negotiations, granted a $100 allowance to smithsons for merchandise purchased on september 25. 29 received payment from smithsons, less allowance and discount. 30 received payment from jordan company, less return.

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The rybczynski theorem describes: (a) how commodity price changes influence real factor rewards (b) how commodity price changes influence relative factor rewards. (c) how changes in factor endowments cause changes in commodity outputs. (d) how trade leads to factor price equalization.