An individual wishes to invest PhP 50,000 over the next year in two types of investment: Investment A yields 5%, and investment B yields 8%. Market research recommends an allocation of at least 25% of the actual total investment in A and at most 50% of the actual total investment in B. Moreover, investment in A should be at least half the investment in B. How should the fund be allocated to the two investments? questions: -Find the feasible region -Find the corner points -Find the optimal value
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An individual wishes to invest PhP 50,000 over the next year in two types of investment: Investment A yields 5%, and investment B yields 8%.
questions:
-Find the feasible region
-Find the corner points
-Find the optimal value
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- 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.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.)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?
- Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: ■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity. ■ At most 10,000 kwh of capacity can be added in a single year. ■ It costs $25 per year to maintain a unit of capacity. ■ It costs $12 per year to produce a kwh. ■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred. Develop a linear integer model to help Hoosier Power minimize its costs for the next 20 years.XYZ Mutual Fund is seeking to invest $80 million in real estate projects with high potential returns. The fund has identified several investment opportunities, each with a specific investment cost and expected economic benefit (see the table below). The goal is to maximize the total economic benefit by selecting a combination of projects to invest in while staying within the budget mentioned above. However, there are several constraints to consider, including the requirement to invest in at least four projects in total, with at least two of them being environmentally friendly (projects that are considered environmentally friendly are: 3, 5, 9, and 10). Additionally, if project 3 is selected, then project 4 must also be chosen, but project 4 can be chosen independently of project 3. The fund cannot make partial or fragmented investments, and projects cannot be purchased multiple times as each project is unique. The challenge is to determine the optimal combination of projects that will…XYZ Mutual Fund is seeking to invest $80 million in real estate projects with high potential returns. The fund has identified several investment opportunities, each with a specific investment cost and expected economic benefit (see the table below). The goal is to maximize the total economic benefit by selecting a combination of projects to invest in while staying within the budget mentioned above. However, there are several constraints to consider, including the requirement to invest in at least four projects in total, with at least two of them being environmentally friendly (projects that are considered environmentally friendly are: 3, 5, 9, and 10). Additionally, if project 3 is selected, then project 4 must also be chosen, but project 4 can be chosen independently of project 3. The fund cannot make partial or fragmented investments, and projects cannot be purchased multiple times as each project is unique. The challenge is to determine the optimal combination of projects that will…
- XYZ Mutual Fund is seeking to invest $80 million in real estate projects with high potential returns. The fund has identified several investment opportunities, each with a specific investment cost and expected economic benefit (see the table below). The goal is to maximize the total economic benefit by selecting a combination of projects to invest in while staying within the budget mentioned above. However, there are several constraints to consider, including the requirement to invest in at least four projects in total, with at least two of them being environmentally friendly (projects that are considered environmentally friendly are: 3, 5, 9, and 10). Additionally, if project 3 is selected, then project 4 must also be chosen, but project 4 can be chosen independently of project 3. The fund cannot make partial or fragmented investments, and projects cannot be purchased multiple times as each project is unique. The challenge is to determine the optimal combination of projects that will…Varma Investment Services must develop an investment portfolio for a new client. As an initial investment strategy, the new client would like to restrict the portfolio to a mix of two stocks: Stock Price/Share Estimated Annual Return (%) AGA Products $ 50 6 Key Energy 100 10 The client wants to invest $50,000 and established the following two investment goals. LO 1, 2A Quezon-city based medium-sized firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 100x1 + 120x2 + 90x3 + 135x4 s.t. 150x1 + 200x2 + 225x3 + 175x4 ≤ 500 {Constraint 1} x1 + x2 + x3 + x4 ≥ 2 {Constraint 2} x2 + x4 ≤ 1 {Constraint 3} x2 + x3 ≥ 1 {Constraint 4} x1 = x4 {Constraint 5} What is the expected net present value of the optimal solution? Group of answer choices
- Your employer is trying to select from a list of possible capital projects. The projects, along with their cost and benefits, are listed below. The capital budget available is $1 million. In addition to spending constraints, your employer would like to select at least 2 projects. Projects 1 and 5 cannot both be selected together. Formulate the problem as a linear program and determine the optimal solution. Project Cost Net Present Value 1 $205,000 $600,000 2 $285,000 $620,000 3 $280,000 $540,000 4 $260,000 $790,000 5 $235,000 $400,000 Which projects should be selected? What is the total net present value of these projects?BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. The advertising budget is $10,000,000. Because BP wants to push its new sodas, at least one-half of the advertising budget is to be devoted to new soda advertising. However, at least $2,000,000 is to be spent on its traditional sodas. BP estimates that each dollar spent on traditional sodas will translate into 100 cans sold, whereas, because of the harder sell needed for new products, each dollar spent on new sodas will translate into 50 cans sold. To attract new customers, BP has lowered its profit margin on new sodas to 2 cents per can as compared to 4 cents per can for traditional sodas. Let X 1 = amount invested in new soda advertising ; and X 2 = amount invested in traditional soda advertising. The objective function that would maximize profit is: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?