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Suppose that a bond portfolio with a duration of 12 years is hedged the use of a futures agreement in which the underlying asset has a duration of 4 years. What is likely to be the impact on the hedge of the reality that the 12-yr rate is less unstable than the 4-yr fee? 6.16. Suppose that it is February 20 and a treasurer realizes that on July 17 the organization will should issue $5 million of commercial paper with a maturity of 180 days. If the paper have been issued today, the corporation could realize $4,820,000. (In other phrases, the enterprise might obtain $four,820,000 for its paper and must redeem it at $5,000,000 in a hundred and eighty days' time.) The September Eurodollar futures rate is quoted as ninety two.00. How have to the treasurer hedge the business enterprise's publicity How can the portfolio supervisor trade the period of the portfolio to 3.Zero years in Problem 6.17? 6.19. Between October 30, 2018, and November 1, 2018, you've got a choice between proudly owning a U.S. Authorities bond paying a 12% coupon and a U.S. Company bond paying a 12% coupon. Consider cautiously the day remember conventions mentioned on this bankruptcy and decide which of the 2 bonds you will favor to own. Ignore the chance of default. 6.20. Suppose that a Eurodollar futures quote is 88 for a agreement maturing in 60 days. What is the LIBOR forward fee for the 60- to a hundred and fifty-day length? Ignore the distinction among futures and forwards for the functions of this query. 6.21. The 3-month Eurodollar futures rate for a settlement maturing in 6 years is quoted as 95.20. The fashionable deviation of the trade in the short-time period interest rate in 1 year is 1.1%. Estimate the forward LIBOR interest rate for the duration among 6.00 and 6.25 years within the future. 6.22. Explain why the forward hobby charge is much less than the corresponding futures hobby price calculated from a Eurodollar futures contract.

[5:41 PM, 10/26/2021] Flo: An excavation contractor deposited 200000 quarterly into a fund paying a nominal interest rate Of 8% per year compounded semiannually For a period of 4 years assume there is no interpolation interest accured . At the end of the fourth year they want to purchase a fleet of trucks for 5000000.The contractor intents to make an immediate cash payment equal amount accumulated and to pay for the rest by equal month end payments. Their financing agreement with the truck dealer is payment should be completed in 18 months and the nominal interest rate should be 18% per year compounded monthly. What will these monthly payments be? Use 4 digits after the decimal point in your interest rate calculation With cash flow diagram [5:53 PM, 10/26/2021] Flo: Illustrate and explain how a firm's short-run demand for labor curve is derived. Also, show and explain that a firm will stop producing in the short-run if the wage rate (w) exceeds the VAP at it's maximum. (hint: a firms will produce in the short-run as long as TR ? TVC). Another hint: You need to show that TR = VAP x E [5:53 PM, 10/26/2021] Flo: The stock price of Obelix and Company is $81.40. At the money call options trade at $2.53, while at the money put options trade at $2.52. You form a straddle from the two options. If the stock price fell, at what price would you start to make a profit?

(b) Give an example of: . An objective function such that both (0,0) and (0, 1.5) are optimal (in minimization form) . An objective function such that only the point (0, 1.5) is optimal (in minimization form). . An objective function such that (LP2) is unbounded (in maximization form). If such an example does not exist, explain why. 2 Problem 3 Consider the following LP: max 10r, + 872 - 313 s.t.: 2x1 + 4.x2 - 0.5x3 6 -2x1 + 6.x2 - 4.503 4 (LP3) I1. T2 free. (a) Write (LP3) in canonical form. If you have to introduce extra variables, explain what they stand for. Compute the initial basic feasible solution and write its value for all of the problem's variables (regardless of whether they are present in the original formulation or introduced for the canonical form).\fProblem 4 "Total 12 points, 3 points each) We want to find valid inequalities for the following 0-1 knapsack problem: max 22r1 + 1012 + 16x3 + 11x4 + 18x5 + 6x6 s.t.: 4x1 + 3x2 + 7x3 + 6x4 + 5rs + 86 : 15 ( KP ) T1, 12, 13, TA, T5, 16 E {0, 1 }. For each of the inequalities below, identify whether or not they are valid. (a) rites + ra S 2. (b) rat ry t r; $ 2. (c) 23 + 25 5 1. (d) 21 + x2 + ra + 16 3. Problem 5 (Total 30 points) We want to solve the following integer program with two variables: max 4x1 + 3.12 s.t.: 2x1 + 12 1 -x1 + 212 LIVIAIA Z'T = CA NOD Let $1, $2 be the slack variables for the first and second constraint respectively. Solving the LP relaxation for this problem yields the following optimal Simplex tableau: Basic $1 Rhs (-2) -11/5 -2/5 -133/5 2/5 -1/5 16/5 1/5 2/5 23/5 (a) (4 points) Slack variables are usually allowed to be fractional. If r, and r2 are both integers, will s, and s2 also be integers? Briefly explain why or why not. (b) (6 points) Derive a Gomory cut from each of the first two rows in the optimal Simplex tableau. (c) (6 points) Express the cuts in terms of the original variables z1 and 12. Graph the feasible region for 21 and 12, and illustrate the cuts on the graph. (d) (6 points) We now append the cuts (or the cut, if only one of them is needed) to the LP relaxation, and resolve. We provide the optimal Simplex tableau after resolving below: Basic $1 X2 $1 $2 $3 Rhs (-2) -2 -26 1/2 -1/2 7/2 1/2 -5/2 3/2 where s3 is the slack variable corresponding to the appended cut. Which rows can be used to derive Gomory cuts? Compute the cuts. Rewrite them in terms of 21 and 12. (e) (8 points) Draw the cuts on your sketch and find the new optimal solution graphically. Is this new solution optimal? (Hint: if you did everything correctly, the new solution is optimal with objective function value 25.)Part 1.A What is the best combination of meals in order to maximize profit? We can assume that meals do not have to be produced in even numbers - that is, we allow a non-integer solution. Write the corresponding Linear Programming formulation on paper, labeling each decision variable and constraint with a proper name (nonnegativity constraints need not be labeled, but do not forget to include them!). Then use Excel to solve the problem. (Hint: the number of Moussaka meals is between 5 and 10 in the optimal solution.) Part 1.B Your little brother offers his help for one hour a day. You assume that he can work as fast as you do, and he can use his bike if needed for delivery, but he can only help with one of the three tasks: cooking, packaging or delivery (not all of them). He asks $10 dollars as a compensation. Should you accept his help? In case of a positive answer, would it be better to ask him to help with cooking, packaging or delivery? (Hint: compute the change in profit if you increase cooking, packaging or delivery time availability by one hour.) Part 1.C There is a drop in the demand of Hummus: instead of 20 meals, only 10 are now requested. Does this change the optimal combination of meals to maximize profit? Could you have guessed without using Excel to solve the new problem? Part 1.D Because you do not want to cook only one kind of meal over and over again, you decide that none of the foods should make up more than 50% of the total portions prepared. How can you add this requirement to the Linear Program defined in Part 1.A (Hint: you may need more than one constraint )? Is the resulting mathematical program still linear? If not, is there a way to write it in linear form?Problem 1 You create your own start-up company that caters high-quality organic food directly to a number of customers. You receive a number of tentative orders and you now have to tell your customers which orders you are going to take. Before embarking on this journey, you first want to allocate your production capabilities in order to devise a feasible daily production plan that maximizes your profit. There are only three different kinds of food that you offer at this early stage of the company: Hummus (H) with garlic pitas, an excellent Moussaka (M), and a traditional Tabouleh (T) with parsley and mint. Each meal has to be cooked, packaged and delivered. Each operation is run by yourself. You have to deliver between 12PM and 2PM everyday, and the food is made on the same day, therefore you estimate that the total number of available cooking hours is 4, the total number of packaging hours is 2, and the total number of delivery hours is 2. Cooking sufficient Hummus for 10 portions requires 1 hour of time, packaging is done at the rate of 20 portions per hour, and delivery at the rate of 30 per hour. The cost of the ingredients for 1 portion is $1, and each packaged portion can be sold for $7. Moussaka takes more time to prepare: in one hour, the food cooking team can prepare 5 portions. Packaging is done at the rate of 15 portions per hour. Since the Moussaka has to be delivered while still warm out of the oven, it is delivered in smaller batches, therefore only 15 portions can be delivered in one hour. The cost of the ingredients for 1 portion is $2, and it can be sold for $12. Finally, Tabouleh can be prepared at the rate of 15 portions per hour, it can be packaged at the rate of 25 portions per hour, and delivered at the rate of 30 per hour. Tabouleh is very inexpensive and one portion only costs $0.5 in raw ingredients, and can be sold for $5. Customers expressed interest in having the following products delivered every day: 20 Hum- mus meals, 10 Moussaka meals, and 30 Tabouleh meals.