revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy.
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)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%.Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.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?PROBLEM 6 An investment firm has $1 million to invest in stocks, bonds, certificates of deposit, and real estate. The firm wishes to determine the mix of investments that will maximize the cash value at the end of 6 years. Opportunities to invest in stocks and bonds will be available at the beginning of each of the next 6 years. Each dollar invested in stocks will return $1.20 (a profit of $0.20) 2 years later; the return can be immediately reinvested in any alternative. Each dollar invested in bonds will return $1.40 3 years later; the return can be reinvested immediately. Opportunities to invest in certificates of deposit will be available only once, at the beginning of the second year. Each dollar invested in certificates will return $1.80 four years later. Opportunities to invest in real estate will be available at the beginning of the fifth and sixth years. Each dollar invested will return $1.10 one year later. To minimize risk, the firm has decided to diversify its…
- Optimization Problem: Emesto is to plant a garden with two types of tree: palms and conifers. He is to plant at least 10, but not more than 80 palms. He is to plant at least 5, but not more than 40 conifers. He cannot plant more than 100 trees in total. Each palm needs 20 litres of water each day and each conifer needs 60 litres of water each day. There are 3000 litres of water available each day. Ernesto makes a profit of €2 on each palm and €1 on each conifer that he plants and he wishes to maximise his profit. Emesto plants x palms and y conifers.George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 5% for the bond fund and 30% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 80% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 6.5%. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Let B = percentage of funds invested in the bond fund S = percentage of funds invested in the stock fundGeorge Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 5% for the bond fund and 30% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 80% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 6.5%. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Let B = percentage of funds invested in the bond fund S = percentage of funds invested in the stock fund fill in the blank 2 B + fill in the blank 3 S s.t.…
- George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 5% for the bond fund and 30% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 80% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 6.5%. Solve the problem using the graphical solution procedure. If required, round the answers to one decimal place.Optimal solution: B = , S = Value of optimal solution is % 2. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Let B = percentage…Fred and Sally Merrit recently inherited a substantial amount of money from a deceased relative. They want to use part of this money to establish an account to pay for their daughter’s college education. Their daughter, Lisa, will be starting college 5 years from now. The Merrits estimate that her first year in college expenses will amount to $12,000 and increase $2,000 per year during each of the remaining three years of her education. The following investments are available to the Merrits: Investment Available Matures Return at Maturity A Every year 1 year 6% B 1, 3, 5, 7 2 years 14% C 1, 4 3 years 18% D 1 7 years 65%