An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file P04_78.xlsx. Gasoline sells for $75 per barrel. Gasoline can have a density of at most 0.95 units per barrel, a viscosity of at most 35 units per barrel, and a sulfur content of at most 3.3 units per barrel. How can the company maximize its profit?
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An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file P04_78.xlsx. Gasoline sells for $75 per barrel. Gasoline can have a density of at most 0.95 units per barrel, a viscosity of at most 35 units per barrel, and a sulfur content of at most 3.3 units per barrel.
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How can the company maximize its profit?
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Describe how the optimal solution to the problem changes as the price of gasoline ranges from $65 to $85 per barrel.
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- In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.You are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)
- CWD Electronics sells Televisions (TV), which it orders from the USA. Because of shipping and handling costs, each order must be for 5TVs. Because of the time it takes to receive an order, the company places an order every time the present stock drops to 5 TVs. It costs $50 to place anorder. It costs the company $500 in lost sales when a customer asks for a TV and the warehouse is out of stock. It costs $100 to keep each TV stored in the warehouse. If a customer cannot purchase a TV when it is requested, the customer will not wait until one comes in but will go to a competitor.The following probability distribution for demand for TV has been and the time required to receive an order once it is placed (lead time) has the following probability distribution: (Attached) The company has 3 TVs in stock. Orders are always received at the beginning of the week.Note that a lead time of 2 weeks imply that an order placed in week one will arrive in week 4. The time required to receive an order…Use excel for this problem A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return. Bond Annual Return Maturity Risk Tax Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free. Formulate the LP model for this problem. Create the spreadsheet model and use Solver to solve the problem.A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the total annual return (before tax). Bond Annual Return Maturity Risk Tax-Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest as least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least 30% of the funds should go in tax-free investments, and at least 40% of the total annual return should be tax free. Suppose the decision variable represents the amount of money invested in bond for . Formulate a linear programming (LP) model to solve the optimal strategy. 1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”. 2. Write down the constraint using the defined decision…
- A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return. Bond Annual Return Maturity Risk Tax Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free. Formulate the LP model for this problem. Create the spreadsheet model and use Solver to solve the problem. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.CWD Electronics sells Televisions (TV), which it orders from the USA. Because of shipping and handling costs, each order must be for 10 TVs. Because of the time it takes to receive an order, the company places an order every time the present stock drops to 5 TVs. It costs $50 to place an order. It costs the company $200 in lost sales when a customer asks for a TV and the warchouse is out of stock. It costs $50 to keep each TV stored in the warehouse. If a customer cannot purchase a TV when it is requested, the customer will not wait until one comes in but will go to a competitor. The following probability distribution for demand for TV has been and the time required to recæive an order once it is placed (lead time) has the following probability distribution: Lead time (weeks) Probability Demand/ week Probability 0.45 0.15 2 0.30 025 0.25 3 0.40 020 The company has 10 TVs in stock. Orders are always received at the beginning of the week. Note that a lead time of 2 weeks imply that an…Why is the RISKCORRMAT function necessary?How does @RISK generate random inputs by default,that is, when RISKCORRMAT is not used?
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