The following table gives the return from 3 activities when 0,1,2,3,4 dollars are invested in each activity. x$ 0 1 2 3 4 r₁(x) 0 4 6 12 13 r2(x) 0 5 8 10 12 13(x) 0 3 7 11 14 (a) Determine the optimal returns when 0,1,2,3 and 4 dollars are invested in all three activities. (b) Determine all the optimal policies when 3 and 4 dollars are invested in all three activities.
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- An investment manager wants to determine an optimal portfolio for a wealthy client. The fund has $2.5 million to invest, and its objective is to maximize total dollar return from both growth and dividiends over the course of the coming year. The client has researched eight high-tech companies and wants the portfolio to consist of shares in these firms only. Three of the firms (S1-S3) are primarily software companies, three (H1-H3) are primarily hardware companies, and two (C1-C2) are internet consulting companies. The client has stipulated that no more than 40% of the investment be allocated to any one of these tree sectors. To assure diversification, at least $100,000 must be invested in each of the eight stocks. The table below gives estimates from the investment company's database relating to these stocks. These es- timates include the price per share, the projected annual growth rate in the share price, and the anticipated annual dividend payment per share. Stock Price per share…M2. The following table provides the basic data of the problem: Tons of raw material per ton of Maximum daily availability (tons) Exterior paint Interior paint Raw material, MI 6 4 24 Raw material, M2 1 2 6 Profit per ton ($1000) 5 4 The daily demand for interior paint cannot exceed that for exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. Reddy Mikks wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the total daily profit. Give the mathematical formula of only the demand constraint? (15 mark) Note for form's designer: design the answer to be as a short paragraph. ا...او10 a b C d e Actions: East, West, and Exit (only available in exit states a, f) Transitions: deterministic For discount factor, y = 1, what is the optimal policy? Use E for East, W for West and X for Exit b. For discount factor, y- 0.5, what is the optimal policy? Use E for East, W for West and X for Exit e 2.
- b. Portfolio B consists of 15 stocks, 10 of which have beta 1 and idiosyncratic variance 0.02, and 5 of which have beta 1 and idiosyncratic variance 0.04. What is the minimum idiosyncratic variance one can achieve by investing in these stocks? You should assume that the idiosyncratic risks of the stocks included in B are independent across stocks. (Hint: the portfolio that minimises the idiosyncratic variance has equal weights in stocks with the same idiosyncratic variance.)Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regularmodel and a catcher’s model. The firm has 900 hours of production time available in itscutting and sewing department, 300 hours available in its finishing department, and100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the table (See image): Assuming that the company is interested in maximizing the total profit contribution, answer the following:a. What is the linear programming model for this problem?b. Find the optimal solution using excel. How many glovesof each model should Kelson manufacture?M2. The following table provides the basic data of the problem: Tons of raw material per ton of Maximum daily availability (tons) Exterior paint Interior paint Raw material, MI 6 4 24 Raw material, M2 2 6 Profit per ton ($1000) 5 4 The daily demand for interior paint cannot exceed that for exterior paint by more than 1 ton. Also. the maximum daily demand for interior paint is 2 tons. Reddy Mikks wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the total daily profit. Give the mathematical formula of only the demand constraint? (15 mark) Note for form's designer: design the answer to be as a short paragraph. 1 اااء
- Activity Dependency Optimistic Most likely Pessimistic A - 5 6 8 B - 3 4 5 C A 2 3 4 D B 1 4 6 E B 1 3 4 F - 8 10 15 G E,F 2 3 4 H C,D 2 2 2.5 By using three estimates for each activity, find: [5[(PL01,PLO3, CLO1, CLO2) Estimated time ‘te” Activity standard deviation ‘s’ Draw PERT network after calculating the event standard deviations.[5]Assume that ABC Company has invested a budget of 36 million riyals for XY project and planned to complete in 12 months. In addition, assume that the company planned to spend the budget equally in each month. However, when the first two months has passed, the project manager has found out that the total of two million riyals spent. Based on the above scenario, answer the following: Suppose Rate of performance =0.25 a) What is the cost variance, schedule variance, cost performance index (CPI), and schedule performance index (SPI) for the project? b) How much will it actually cost the company to complete this project, and how long will it really take to complete it based on the performance to date? c) What do you think of the project performance? over/under the budget? behind /ahead the schedule? Justify your answer.A variable that assumes an optimal value between its lower and upper bounds has a reduced cost value of zero. Why must this be true? (Hint: What if such a variable’s reduced cost value is not zero? What does this imply about the value of the objective function?)
- MRDL Co.'s bonds, issued 8 years ago, currently sell for $1,123. They have a 9.64% semi-annual coupon rate and a 30-year maturity, a $1,000 par value, and are callable in 10 years from the issue date at $1,065.00. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels in the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds, 8 years after the issue? O 6.1173 % 8.5004% 3.2390% 06.0779 % O 8.4043 %If you have a column of cash flows from years 0 to n and you wish to calculate the present worth of the cash flows. You could use the following EXCEL function(s) for solving the problem with an excel spread sheet: None of the above Maximize EUAB Maximize NPW Maximize (EUAB - EUAC) Maximize PW of Benefits3. Consider the following graph for question a and b. 8 E (a) What is the highest-cost path for finding the goal G? (b) What is the lowest-cost path for finding the goal G?