(Do not factor.)The maximum number of viewers is. In order to get that number of viewers, there should beminutes of sports, minutes of news, andminutes of weather.(Type whole numbers.)(b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem.When viewership is maximized, s, =means thatV of thek vailable 45 minutes were used; s2 =|means that sports hadV twice as much time as the weather; and sa = means that the sports andthe weather had a total timeV twice the time of the news. A local news channel plans a 45-minute Saturday morning news show. The show will be divided into three segments involving sports, news, and weather. Market research has shown that the sports segment should betwice as long as the weather segment. The total time taken by the sports and weather segments should be twice the time taken by the news segment. On the basis of the market research, it is believed that 50, 65, and 60(in thousands) viewers will watch the program for each minute the sports, news, and weather segments, respectively, are on the air. Use the simplex method to complete parts (a) and (b).(a) Find the time that should be allotted to each segment in order to get the maximum number of viewers. Find the number of viewers.Set up the linear programming problem. Let x,, X2, and x, be the number of minutes taken by the sports, news, and weather segments, respectively, and let z be the number of viewers in thousands.V z=subject toX4 + X2 + X3-X, + 2x3-X1 +2x2 - X3

x1,x2 and x3 are number of minutes taken by sports, news and weather segments respectively. Our…

Answered: The maximum number of viewers is In…

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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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.
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
Harvesting Fruit Toward the middle of the harvesting sea-son, peaches for canning come in three types, early, late, and extra late, depending on the expected date of ripening. During a certain week, the following data were recorded at a fruit delivery station:34 trucks went out carrying early peaches;61 carried late peaches;50 carried extra late;25 carried early and late;30 carried late and extra late;8 carried early and extra late;6 carried all three;9 carried only fgs (no peaches at all).(a) How many trucks carried only late variety peaches?(b) How many carried only extra late?(c) How many carried only one type of peach?(d) How many trucks (in all) went out during the week?
KAPC, a pharmaceutical company located in rural Kansas, is finding it difficult to retain its employees, who frequently leave after just six months of working at KAPC for jobs at pharmaceutical companies paying higher wages in Chicago. To address its problem with labor turnover, human resource officers at KAPC decide to run an experiment. Of their next 100 newly hired employees, 25 will randomly be selected to receive a housing voucher worth up to $4,000 per year to offset property taxes. To take advantage of this program, the employee must not only be randomly selected into the program but she must also purchase a home. Of the 25 employees selected into the housing voucher program, 7 leave KAPC within 12 months of starting. Of the 75 employees not selected into the program, 37 leave KAPC within 12 months of starting.a. Provide a difference-in-differences estimate of the effect the housing voucher program has on retention at KAPC.b. Suppose KAPC spends $10,000 in hiring costs each time…
Harvesting Fruit Toward the middle of the harvesting sea-son, peaches for canning come in three types, early, late, and extra late, depending on the expected date of ripening. During a certain week, the following data were recorded at a fruit delivery station:34 trucks went out carrying early peaches;61 carried late peaches;50 carried extra late;25 carried early and late;30 carried late and extra late;8 carried early and extra late;6 carried all three;9 carried only fgs (no peaches at all). (a) How many trucks carried only late variety peaches?(b) How many carried only extra late?(c) How many carried only one type of peach?(d) How many trucks (in all) went out during the week? with a venn diagram
A political party is planning a half-hour television show. The show will have at least 3 minutos of direct requests for money from viowers Three of the party's politicians will be on the show-a senator, a congresswoman, and a governor The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor The total time taken by the senator and the governor must be at least twice the time taken y the congresswoman Based on a pre-show survey, it is believed that 33, 38, and 43 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers Find the maximum number of viewers The quantity to be maximized, z, is the number of viewers in thousands. Let x, be the total number of minutes allotted to the senator, x, be the total number of minutes allottod to the congresswoman, and x,…
Ensemble Theatre of Cincinnati D. Lynn Meyers has been Producing Artistic Director of the nationally renowned Ensemble Theatre of Cincinnati (ETC) since 1995. The nonprofit ETC, recently celebrating its 25th anniversary, is dedicated to the production and development of new plays and of works new to the region. Lynn values the opinions of each member of her small staff when hiring. She usually interviews four or five people for a staff position and conducts two interviews. After the preliminary interview determines that an applicant is suitable, she says, “We invite the person back to meet the staff they would have contact with on a daily basis.” She has passed on qualified candidates who did not interact well with their prospective coworkers or who did not convince her that they had a strong desire for the job. Lynn researches job applicants online and on social media sites. “Frankly, if we find unprofessional behavior, we take that into consideration,” she says. “We always check…
A retail store sold in the month of April 5,000 products that produced $45,000 in sales. In the month of May the company sold 6,000 products. The store workforce consists of four full-time workers who work 40-hour week. In April the store also had seven part-time workers at 10 hours per week, and in May the store had nine part-timers at 15 hours per week (assume four weeks in each month). Using sales dollars as the measure of output (assume the price of the product was the same for both months), what is the percentage change in labor productivity from April to May? Answer: 2.
Ensemble Theatre of Cincinnati D. Lynn Meyers has been Producing Artistic Director of the nationally renowned Ensemble Theatre of Cincinnati (ETC) since 1995. The nonprofit ETC, recently celebrating its 25th anniversary, is dedicated to the production and development of new plays and of works new to the region. Lynn values the opinions of each member of her small staff when hiring. She usually interviews four or five people for a staff position and conducts two interviews. After the preliminary interview determines that an applicant is suitable, she says, “We invite the person back to meet the staff they would have contact with on a daily basis.” She has passed on qualified candidates who did not interact well with their prospective coworkers or who did not convince her that they had a strong desire for the job. Lynn researches job applicants online and on social media sites. “Frankly, if we find unprofessional behavior, we take that into consideration,” she says. “We always check…
Ensemble Theatre of Cincinnati D. Lynn Meyers has been Producing Artistic Director of the nationally renowned Ensemble Theatre of Cincinnati (ETC) since 1995. The nonprofit ETC, recently celebrating its 25th anniversary, is dedicated to the production and development of new plays and of works new to the region. Lynn values the opinions of each member of her small staff when hiring. She usually interviews four or five people for a staff position and conducts two interviews. After the preliminary interview determines that an applicant is suitable, she says, “We invite the person back to meet the staff they would have contact with on a daily basis.” She has passed on qualified candidates who did not interact well with their prospective coworkers or who did not convince her that they had a strong desire for the job. Lynn researches job applicants online and on social media sites. “Frankly, if we find unprofessional behavior, we take that into consideration,” she says. “We always check…
Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The city has been broken down into 20 geographic areas, each containing 5,000 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 800 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) The 800…
Ensemble Theatre of Cincinnati D. Lynn Meyers has been Producing Artistic Director of the nationally renowned Ensemble Theatre of Cincinnati (ETC) since 1995. The nonprofit ETC, recently celebrating its 25th anniversary, is dedicated to the production and development of new plays and of works new to the region. Lynn values the opinions of each member of her small staff when hiring. She usually interviews four or five people for a staff position and conducts two interviews. After the preliminary interview determines that an applicant is suitable, she says, “We invite the person back to meet the staff they would have contact with on a daily basis.” She has passed on qualified candidates who did not interact well with their prospective coworkers or who did not convince her that they had a strong desire for the job. Lynn researches job applicants online and on social media sites. “Frankly, if we find unprofessional behavior, we take that into consideration,” she says. “We always check…

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