The english coinage before decimalization included half-crowns (30 pence), florins (24 pence), shillings (12 pence), sixpences (6 pence), threepences (3 pence), and pennies (not to mention ha’pennies and farthings, worth respectively ½ and ¼ pence). show that with these coins the greedy algorithm does not necessarily produce an optimal solution, even with an unlimited supply of coins of each denomination is available. 

Bond x is noncallable and has 20 years to maturity, a 7% annual coupon, and a $1,000 par value. your required return on bond x is 10%; if you buy it, you plan to hold it for 5 years. you (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 9.5%. how much should you be willing to pay for bond x today? (hint: you will need to know how much the bond will be worth at the end of 5 years.) do not round intermediate calculations. round your answer to the nearest cent.

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Consider the market for gasoline. suppose that, in a competitive market without government regulations, the equilibrium price of gasoline is $3.00 per gallon, and employees at gas stations earn $17.50 per hour. complete the following table by indicating whether each of the statements is an example of a price ceiling or a price floor and whether it results in a shortage or a surplus or has no effect on the price and quantity that prevail in the market. statement price control effect the government has instituted a legal minimum price of $3.40 per gallon for gasoline. the government prohibits gas stations from selling gasoline for more than $3.40 per gallon. due to new regulations, gas stations that would like to pay better wages in order to hire more workers are prohibited from paying more than $14.50 per hour.