Define the decision variables ,Formulate the objective function, Formulate the constraints Sears Investment has $250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Bank regulations require diversification to the extent that a t least 50% of the investment be placed in Treasury notes. Because of defaults in such municipalities as California and Texas, it is decided that no more than 40% of the investment be placed in bonds. How much should Sears Investment invest in each security so as to maximize its return on investment?
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Define the decision variables ,Formulate the objective function, Formulate the constraints
Sears Investment has $250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average
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- The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.Please answer this using EXEL AND SOLVER ADD IN. Include and identify decision variables, objective, and constraints. Please also upload what the info in solver you added was!!!! It is summertime and your winter coat factory is trying to decide its production schedule and staffing level for the next season. You are forecasting demand of 5000 coats in October, 8000 coats in November, 8000 coats in December, 12000 coats in January, 12000 coats in February and 9000 coats in March. You want to manufacture these coats at the lowest cost possible during your production window (October-March). The first decision you need to make is how many people to hire. Each employee will cost $2500 a month. You don’t want to hire or fire any employees mid-season in order to minimize disruptions in your factory floor. You can have employees idle if there isn’t sufficient work for them to do. Employees still need to be paid even if they are idle. An employee works 20 business days a month and takes half a…Northwest Pipe (NP) makes water pipe. NP is planningproduction for the next seven months, March through September.Th e forecast demands (in thousands of feet) are, respectively, 40,60, 70, 80, 90, 100, and 80. NP can make 75,000 feet of pipe permonth using regular-time production, at a cost of $1.25 per foot.Th ey can make up to an additional 15,000 feet using overtimeproduction at a cost of $1.50 per foot. Any pipe made in onemonth and sold in a later month incurs an inventory holding costof $0.15 per foot, per month. NP expects to end February with5000 feet of pipe and would like to plan to end September with10,000 feet in inventory. NP would like to plan their productionschedule to minimize total cost during the next seven months. (a) Formulate an LP to minimize total costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution
- Always Rain Irrigation, Inc., would like to determine capacity requirements for the next four years to make three types of bronze sprinklers: 90-degree nozzle sprinklers, 180-degree nozzle sprinklers, and 360-degree nozzle sprinklers. Management has forecast demand for the next 4 years as follows: Yearly Demand in 000's: Year 1, Year 2, Year 3, Year 4: Bronze 90: 7, 8, 9, 10 Bronze 190: 3, 4, 5, 6 Bronze 360: 11, 12, 15, 18 The machines needed for the bronze sprinklers require two operators, and can produce up to 12,000 sprinklers. Three bronze machines and only one injection molding machine are available. What are the capacity requirements for the next four years, assume that there is no learning? Capacity: Year 1, Year 2, Year 3, Year 4: Demand for bronze sprinklers: Percentage of capacity used: Machine requirements: Labor requirements:A linear programming computer package is needed. The Silver Star Bicycle Company will be manufacturing both men's and women's models for its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 200 men's and 150 women's models to be shipped during the second month. Additional data are shown. Model Production Costs Labor Requirements (hours) Current Inventory Manufacturing Assembly Men's $120 2.0 1.5 20 Women's $90 1.6 1.0 30 Last month the company used a total of 1,000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the…Formulate the Linear Programming algebraic model : The DLSU Faculty Cooperative has P250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Cooperatives regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of restrictions of Bureau of Internal Revenue, it is decided that no more than 40% of the investment be placed in bonds. Determine the budget that should be allocated
- 3) A brokerage firm has been tasked with investing $500,000 for a new client. The client has asked that the broker select promising stocks and bonds for investment, subject to the following guidelines: at least 20% in municipal bonds, at least 10% each in real estate and pharmaceutical stock, and at least 40% in a combination of energy and domestic automobile stocks with each accounting for at least 15%. The returns are as follows: Municipal = 5.3%, Domestic Automobile = 8.8%, Energy = 4.9%, Pharmaceuticals = 8.4% and Real Estate = 10.4%. a) Write a linear program complete with objective function and all constraints to Maximize the return. (5 points) b) What is the optimal solution? Give values for all variables rounded to the nearest cent.(2 points) c) How much annual income does the optimal solution generate? (2 points) d) Submit your excel workbook. (2 points)Mr Chan lives with his parents in Aberdeen. He owns a flat in causeway bay. The order of preference of ways for him to use his flats as follow 1st choice: run a restaurant. 2nd choice: rent it out. 3rd choice: live in it. Explain how the cost of using the flat to run the restaurant maybe affected if, a. The market rental rate sharply increases. b. His parents health deteriorates and there is an increasing need for him to take care of them. c. He has employed a cook at a salary lower than the market rateA car company is planning the introduction of a new electric car. There are two options for production. One is to produce the electric car at the company’s existing plant in Illinois, sharing production with its other products that are currently being produced there. If the sales of the electric car are moderate, this will work out well as there is significant capacity to produce all of the products there. However, if sales of the electric car are strong, this option would necessitate Adding a 3rd shift, which would lead to significantly higher costs. Another option is to build a new plant in Ohio. The new plant would have sufficient capacity to meet whatever level of demand for the new car. However, if sales of the new car not strong, the plant would be underutilized and less efficient. Since this is a new product, sales are hard to predict. The forecast indicates there is a 60% chance of strong sales (annual sales of 100,000), and 40% chance of moderate sales (annual sales of…
- Mrs. Z, vice president for operations of XY, Inc., a manufacturer of imaginary product T, is constrained from meeting her 5-year forecast by limited capacity at the company’s two existing facilities, which are in San Diego, California (F1) and Grenville, South Carolina (F2). As her able assistant, you have been told that because of existing capacity constraints and the expanding market for the company’s product, a third plant is to be added. The real estate department has advised Mrs. Z that two potential sites seem particularly good, located in Waco, Texas (F3), and Norfolk, Nebraska (F4). The company ships the products to three demand markets in East (M1), Mid-West (M2), and West (M3), via its two cross-docking distribution centers in Colorado (D1) and Kentucky (D2). You are asked to find the optimal distribution strategy that will determine where the third facility be located (F3 or F4), and the best distribution pattern across the supply chain. The company consider the…Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?Company X is planning to run a project that requires an initial investment of RM 80,000.Operation cost is estimated at RM 20,000 per year starting one year from the start of theproject until its project life. Starting second year onwards, the operation cost is expectedto increase by RM 5,000 from previous year. The project will start to generate its annualincome of RM 70,000 on the second year until fifth year. The salvage value of the projectis RM 50,000 and its project life is five years. a) Construct the cash flow diagram to summarize the above transactions. b) Determine the expected project value at the end of five years. Assume the growth rateis 12%.