1. Gina's target population for her study are employees from the top 500 corporations in the Philippines. Because there are too many employees in these corporations, she decided to randomly select ten corporations, she decided to randomly select ten corporations and use all of their employees as participants in her study. 2. Myra's study aims to determine the relationship between intelligence quotient and the language proficiency of students. There are 105,000 students in her target population. Of these, 15% have high proficiency, 65% have average proficiency, and 20% have low proficiency. She decided to utilize a sample size of 400 participants from the target population. This is proportional to the total number of members in each group of the population.

1. Gina's target population for her study are employees from the top 500 corporations in the Philippines. Because there are too many employees in these corporations, she decided to randomly select ten corporations, she decided to randomly select ten corporations and use all of their employees as participants in her study. 2. Myra's study aims to determine the relationship between intelligence quotient and the language proficiency of students. There are 105,000 students in her target population. Of these, 15% have high proficiency, 65% have average proficiency, and 20% have low proficiency. She decided to utilize a sample size of 400 participants from the target population. This is proportional to the total number of members in each group of the population.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section4.8: Data Envelopment Analysis (dea)

Problem 43P

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You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).
The eTech Company is a fairly recent entry in the electronic device area. The company competes with Apple. Samsung, and other well-known companies in the manufacturing and sales of personal handheld devices. Although eTech recognizes that it is a niche player and will likely remain so in the foreseeable future, it is trying to increase its current small market share in this huge competitive market. Jim Simons, VP of Production, and Catherine Dolans, VP of Marketing, have been discussing the possible addition of a new product to the companys current (rather limited) product line. The tentative name for this new product is ePlayerX. Jim and Catherine agree that the ePlayerX, which will feature a sleeker design and more memory, is necessary to compete successfully with the big boys, but they are also worried that the ePlayerX could cannibalize sales of their existing productsand that it could even detract from their bottom line. They must eventually decide how much to spend to develop and manufacture the ePlayerX and how aggressively to market it. Depending on these decisions, they must forecast demand for the ePlayerX, as well as sales for their existing products. They also realize that Apple. Samsung, and the other big players are not standing still. These competitors could introduce their own new products, which could have very negative effects on demand for the ePlayerX. The expected timeline for the ePlayerX is that development will take no more than a year to complete and that the product will be introduced in the market a year from now. Jim and Catherine are aware that there are lots of decisions to make and lots of uncertainties involved, but they need to start somewhere. To this end. Jim and Catherine have decided to base their decisions on a planning horizon of four years, including the development year. They realize that the personal handheld device market is very fluid, with updates to existing products occurring almost continuously. However, they believe they can include such considerations into their cost, revenue, and demand estimates, and that a four-year planning horizon makes sense. In addition, they have identified the following problem parameters. (In this first pass, all distinctions are binary: low-end or high-end, small-effect or large-effect, and so on.) In the absence of cannibalization, the sales of existing eTech products are expected to produce year I net revenues of 10 million, and the forecast of the annual increase in net revenues is 2%. The ePIayerX will be developed as either a low-end or a high-end product, with corresponding fixed development costs (1.5 million or 2.5 million), variable manufacturing costs ( 100 or 200). and selling prices (150 or 300). The fixed development cost is incurred now, at the beginning of year I, and the variable cost and selling price are assumed to remain constant throughout the planning horizon. The new product will be marketed either mildly aggressively or very aggressively, with corresponding costs. The costs of a mildly aggressive marketing campaign are 1.5 million in year 1 and 0.5 million annually in years 2 to 4. For a very aggressive campaign, these costs increase to 3.5 million and 1.5 million, respectively. (These marketing costs are not part of the variable cost mentioned in the previous bullet; they are separate.) Depending on whether the ePlayerX is a low-end or high-end produce the level of the ePlayerXs cannibalization rate of existing eTech products will be either low (10%) or high (20%). Each cannibalization rate affects only sales of existing products in years 2 to 4, not year I sales. For example, if the cannibalization rate is 10%, then sales of existing products in each of years 2 to 4 will be 10% below their projected values without cannibalization. A base case forecast of demand for the ePlayerX is that in its first year on the market, year 2, demand will be for 100,000 units, and then demand will increase by 5% annually in years 3 and 4. This base forecast is based on a low-end version of the ePlayerX and mildly aggressive marketing. It will be adjusted for a high-end will product, aggressive marketing, and competitor behavior. The adjustments with no competing product appear in Table 2.3. The adjustments with a competing product appear in Table 2.4. Each adjustment is to demand for the ePlayerX in each of years 2 to 4. For example, if the adjustment is 10%, then demand in each of years 2 to 4 will be 10% lower than it would have been in the base case. Demand and units sold are the samethat is, eTech will produce exactly what its customers demand so that no inventory or backorders will occur. Table 2.3 Demand Adjustments When No Competing Product Is Introduced Table 2.4 Demand Adjustments When a Competing Product Is Introduced Because Jim and Catherine are approaching the day when they will be sharing their plans with other company executives, they have asked you to prepare an Excel spreadsheet model that will answer the many what-if questions they expect to be asked. Specifically, they have asked you to do the following: You should enter all of the given data in an inputs section with clear labeling and appropriate number formatting. If you believe that any explanations are required, you can enter them in text boxes or cell comments. In this section and in the rest of the model, all monetary values (other than the variable cost and the selling price) should be expressed in millions of dollars, and all demands for the ePlayerX should be expressed in thousands of units. You should have a scenario section that contains a 0/1 variable for each of the binary options discussed here. For example, one of these should be 0 if the low-end product is chosen and it should be 1 if the high-end product is chosen. You should have a parameters section that contains the values of the various parameters listed in the case, depending on the values of the 0/1 variables in the previous bullet For example, the fixed development cost will be 1.5 million or 2.5 million depending on whether the 0/1 variable in the previous bullet is 0 or 1, and this can be calculated with a simple IF formula. You can decide how to implement the IF logic for the various parameters. You should have a cash flows section that calculates the annual cash flows for the four-year period. These cash flows include the net revenues from existing products, the marketing costs for ePlayerX, and the net revenues for sales of ePlayerX (To calculate these latter values, it will help to have a row for annual units sold of ePlayerX.) The cash flows should also include depreciation on the fixed development cost, calculated on a straight-line four-year basis (that is. 25% of the cost in each of the four years). Then, these annual revenues/costs should be summed for each year to get net cash flow before taxes, taxes should be calculated using a 32% tax rate, and taxes should be subtracted and depreciation should be added back in to get net cash flows after taxes. (The point is that depreciation is first subtracted, because it is not taxed, but then it is added back in after taxes have been calculated.) You should calculate the company's NPV for the four-year horizon using a discount rate of 10%. You can assume that the fixed development cost is incurred now. so that it is not discounted, and that all other costs and revenues are incurred at the ends of the respective years. You should accompany all of this with a line chart with three series: annual net revenues from existing products; annual marketing costs for ePlayerX; and annual net revenues from sales of ePlayerX. Once all of this is completed. Jim and Catherine will have a powerful tool for presentation purposes. By adjusting the 0/1 scenario variables, their audience will be able to see immediately, both numerically and graphically, the financial consequences of various scenarios.
A large CPA firm currently has 100 junior staffmembers and 20 partners. In the long run—say,20 years from now—the firm would like to consistof 130 junior staff members and 20 partners. During a given year, 10% of all partners and 30% ofall junior staff members leave the firm. The firmcan control the number of hires each year and thefraction of junior employees who are promoted topartner each year. Can you develop a personnelstrategy that would meet the CPA firm’s goals?
A soup company wants to determine the optimal ingredients for its vegetable soup. The main ingredients are: Vegetables, Potatoes, Carrots, Onions, Meat, Water, Flavorings. The soup must meet the following specifications: A. No more than half of the soup can be vegetables B. The ratio of water to meat should be 8:1 C. The amount of meat should be between 5 & 6 percent of the soup D. The flavorings should weigh no more than ½ ounce The cost per ounce of the ingredients is $0.02 for the vegetables, $0.05 for the meat, $0.001 for water, and $0.05 for the flavorings. Formulate an LP model that will determine the optimal amounts of the various ingredients to achieve 15-ounce cans of soup at minimum cost
KrazySockzThe KrazySockz Company is known for their colorful yetcomfortable socks. They have forecasted their demand for the nextsix months as follows: Month 1 demand is 30,000, month 2demand is 50,000, month 3 demand is 20,000, month 4 demand is10,000, month 5 demand is 15,000 and month 6 demand is 20,000.At the beginning of month 1 they have 15,000 pairs of socks onhand. KrazySockz currently has 40 production employees. Each productionemployee costs the company the company $4,000 per month ($3,200 salary and $800in other costs) per month. Production employees can work up to 160 hours permonth before they must be paid overtime. Overtime is paid at a rate of $30 per hourand production employees can not work more than 30 hours per month overtime. Ittakes 15 minutes of labor and $0.75 of raw material to produce a pair of socks.KrazySockz can hire or fire employees each month. Hiring a production employeeincurs a cost of $3,500 and firing a production employee costs $4,500. At the end…
This problem does not require the use of data mining software and focuses on knowledge of concepts and basic calculations. Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters (in standardized units), describing the average characteristics of a wine in each cluster, are listed in the following table. Characteristic Cluster 1 Cluster 2 Cluster 3 Alcohol 0.819 0.164 −0.937 Malic Acid −0.329 0.869 −0.368 Ash 0.248 0.186 −0.393 Alkalinity −0.677 0.523 0.249 Magnesium 0.643 −0.075 −0.573 Phenols 0.825 0.977 −0.034 Flavonoids 0.896 −1.212 0.083 Nonflavonoids −0.595 0.724 0.009 Proanthocyanidins 0.619 −0.778 0.010 Color Intensity 0.135 0.939 −0.881 Hue 0.497 −1.162 0.437 Dilution 0.744 −1.289 0.295 Proline 1.117 −0.406 −0.776 Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should Jay place this new wine? Justify your choice with appropriate…
The Bluegrass Distillery produces custom-blended whiskey. A particular blend consists of rye and bourbon whiskey. The company has received an order for a minimum of 300 gallons of the custom blend. The customer specified that the order must contain at least 40% rye and not more than 280 gallons of bourbon. The customer also specified that the blend should be mixed in the ratio of rye to bourbon as 2 to 1 (i.e. rye:bourbon=2:1). The distillery can produce 500 gallons per week, regardless of the blend. The production manager wants to complete the order in 1 The blend is sold for $5 per gallon. The distillery company’s cost per gallon is $2 for rye and $1.5 for bourbon. The company wants to determine the blend mix that will meet customer requirements and maximize profits. Formulate a linear programming model for this problem. Solve the problem by using the computer
Below is an excerpt from the article: Bennett, R. (2005). Factors associated with student plagiarism in a post-1992 university. Assessment & Evaluation in Higher Education, 30, 137-162.“There is a need for university staff to address forcefully the issue of academic integrity during introductory programs and to explain clearly and sympathetically the objective need for honesty in academic life” (p. 156).Which of the following examples correctly paraphrases the above passage without plagiarizing? Select one: a. During orientations, university staff should be very clear about the importance of academic integrity (Bennett, 2005). b. There is a need for colleges to forcefully address the issue of academic integrity during beginning programs and to explain clearly and sympathetically the objective need for integrity in college life (Bennett, 2005). c. There is a need for university staff to address forcefully the issue of academic integrity during introductory programs and to explain…
Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 7x + 14y + 4z subject to the following. 3x + 5y + 4z ≤ 30 3x + 2y ≤ 4 x + 2y ≤ 8 (x,y,z)= f=
8-2 (Investment decision problem) The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated but within the following guidelines: Municipal bonds should constitute at least 20% of the investment. At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers. No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock. Use Solver to solve the problem. You need to have one Excel sheet with the problem setup and another sheet with Solver solution subject to these restraints, the client’s goal…
Thomas has eight horses averaging 1,400 pounds. They are on 20 acres of orchard grass and clover. Each year, Thomas applied 30-30-30 units of fertilizer per acre using 46-0-0 urea at $408 per ton, 18-46-0 DAP at $496 per ton, and 0-0-60 muriate of potash at $506 per ton. He reseeded with 10 pounds per acre of orchard grass at $1.19 per pound and 2 pounds per acre of clover at $3.18 per pound. The horses are housed in a barn 34 feet wide with stalls 12 by 12 feet on each side and a 10-foot aisle down the center. He needs at least one fifth of the barn, not including the center, for hay and tack room. What did it cost to fertilize and reseed the pasture? How long must he barn be in even number of feet?
Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…