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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?A company is considering a new product launch. There is a 0.6 chance that demand for the product will be strong and a 0.4 chance that demand will be weak. Two strategies for the launch are possible: 1 has high promotion costs and a net cash outflow of K120 000 if demand proves to be strong, and if demand proves weak a net cash outflow of (K30 000) will result. Strategy 2 has low promotion costs and if demand is strong will generate a cash inflow of only K80 000 but with weak demand a net cash inflow of K20 000. Draw a decision tree and advise which course of action generates the greatest expected profit. What is the maximum amount that should be paid for market research to determine with certainty whether demand will be strong or weak?
- Formulate an LP model for the following problems.1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit orboth. The Best Fund pays 8% per year and the time deposit pays 9%. Because theBest Fund is riskier than the time deposit, so she intends to put at most ₱30,000 intothe time deposit and at least ₱10,000 into the Best Fund. How much should she allotto each investment in order to maximize her returns?A business student has $3,500 available from a summer job and has identified three potential stocks in which to invest. The cost per share and expected return over the next two years are given in the table. Complete parts a and b. A $12 $8 Stock Price/share Return/share B $16 $5 A. Amount invested in stock A B. Amount invested in stock B C. Return for each stock D. Amount invested in stock C E. Price of each stock C $25 $11 a. Identify the decision variables, objective function, and constraints in simple verbal expressions. Identify the decision variables. Select all that apply.An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profits, in Kwacha, of each investment under each economic condition are indicated in the following payoff table: Event Investment selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000 Based on his own past experience, the investor assigns the following probabilities to each economic condition: P (Economy declines) = 0.30 P (No Change) = 0.50 P (Economy expands) = 0.20 i. Compute the coefficient of variation for each investment. ii. Compute the return-to-risk ratio (RTRR) for each investment. iii. Based on (i) and (ii), what investment would you choose? Why?
- 3. The comptroller of Microsoft Corporation has $100 million of excess funds to invest. She has been introduced to invest the entire amount for one year in either stocks or bonds (but not both) and then to reinvest the entire fund in either stocks or bonds (but not both) for one year more. The objective is to maximize the expected monetary value of the fund at the end of the second year. The annual rates of return on these investments depend on the economic environment, as shown in the following table: Rate of Return Economic Environment Stocks Bonds Growth 20% 5% Recession -10% 10% Depression -50% 20% The probabilities of growth, recession, and depression for the first year are 0.7, 0.3, and 0, respectively. If growth occurs in the first year, these probabilities remain the same for the second year. However, if a recession occurs in the first year, these probabilities change to 0.2, 0.7, and 0.1, respectively, for the second year. Construct the decision tree for this problem and…After a successful newspaper business, Jimmy plans to expand by opening an icrecream shop, only if there is a good chance of making a profit. He can open a small shop, a large shop, or no shop at all. Bulding leases are five years long so he wants to make a good decision. Jimmy has done some market research and has found with a large shop he will earn $60 000 in a good market but will lose $40 000 if the market is bad. A small shop will earn him thirty thousand dollars in a good market but will lose ten thousand dollars in a bad market. Present indications are that there is a fifty-nice percent chance of a good market. Jimmy also has the option of hiring his friend for five thousand dollars to conduct a marketing research study. If the study is conducted. With the survey, there is a sixty percent probability that it will be favourable. Also, there is a ninety percent chance of a good market if the survey is favourable. However, there is also twelve percent probability of a good market…An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profit in Kwacha of each investment under each economic condition are indicated in the following payoff table: Event Investment Selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000 Based on his own past experience, the investor assigns the following probabilities to each economic condition: ( ) ( ) ( ) Economy declines 0.30 No change 0.50 Economy expands 0.20PPP=== i. Determine the optimal action based on the maximax criterion ii. Determine the optimal action based on the maximin criterion iii. Compute the expected monetary value (EMV) for each investment
- An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profit in Kwacha of each investment under each economic condition are indicated in the following payoff table: Event Investment Selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000 Based on his own past experience, the investor assigns the following probabilities to each economic condition: ( ) ( ) ( ) Economy declines 0.30 No change 0.50 Economy expands 0.20PPP=== iv. Compute the expected opportunity loss (EOL) for each investment v. Explain the meaning of the expected value of perfect information (EVPI) in this problem vi. Based on the results of (iii) and (iv), which investment would you choose? Why?Managing a Portfolio. A local bank wants to build a bond portfolio from a set of five bonds with $1 million available for investment. The expected annual return, the worst-case annual return on each bond, and the “duration” of each bond are given in the following table. (The duration of a bond is a measure of the bond’s sensitivity to changes in interest rates.)Expected Return Worst Case Return DurationBond 1 12.5% 8.0% 8Bond 2 11.5% 7.5% 7Bond 3 10.5% 6.8% 6Bond 4 9.5% 7.0% 5Bond 5 8.5% 7.4% 3The bank wants to maximize the expected return from its bond investments, subject to three conditions: The average worst-case return for the portfolio must be at least 7.2 percent.The average duration of the portfolio must be at most 6.Because of diversification requirements, at most 40 percent of the total amount invested can be invested in a single bond.What is the maximum return on the $1 million investment? How should the investment be…Consider an investment project with the following cash flows: N Cash Flow 0 -$5,0001 $02 $4,8403 $1,331ComputcthelRRforthisinvestment.lsthisprojectacceptablcatMARR = 10%?