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- Suppose that GLC earns a 2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLCs cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then purchase a car every five yearsduring year 6, year 11, and so on. For simplicity, we assume that Hundo is GLCs only competitor. We also assume that if the consumer is satisfied with the car she purchases, she will buy her next car from the same company, but if she is not satisfied, she will buy her next car from the other company. Hundo produces cars that satisfy 80% of its customers. Currently, GLC produces cars that also satisfy 80% of its customers. Consider a customer whose first car is a GLC car. If profits are discounted at 10% annually, use simulation to estimate the value of this customer to GLC. Also estimate the value of a customer to GLC if it can raise its customer satisfaction rating to 85%, to 90%, or to 95%. You can interpret the satisfaction value as the probability that a customer will not switch companies.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 company manufactures two types of trucks. Eachtruck must go through the painting shop and the assembly shop. If the painting shop were com-pletely devoted to painting type 1 trucks, 650 per day could be painted, whereas if the painting shopwere completely devoted to painting type 2 trucks,550 per day could be painted. If the assembly shopwere completely devoted to assembling truck 1engines, 1400 per day could be assembled, whereasif the assembly shop were completely devoted toassembling truck 2 engines, 1000 per day could beassembled. It is possible, however, to paint bothtypes of trucks in the painting shop. Similarly, it ispossible to assemble both types in the assemblyshop. Each type 1 truck contributes $2500 to profit; each type 2 truck contributes $3000. Use Solver to maximize the company’s profit. (Hint: One ap-proach, but not the only approach, is to try a graphi-cal procedure first and then deduce the constraints from the graph.)
- At modern woodworks, president and producer of apple crates sold to growers, has been able, with his current equipment, to produce 240 crates per 100 logs. He currently purchases 100 logs per day, and each log requires 3 labor hours to process. He believes that he can hire a profesional buyer who can buy a better quality log at the same cost. if this is the case, he can increase hos production to 260 crates per 100 logs. His labour-hours will increase by 8 hours per day. What will be the impact on productivity (measured in crates per labor-hour) if the buyer is hired?A call center employs 1,425 agents. Every month 57 employees leave the company and 57 new employees are hired. a. How long on average does an agent work for this call center (in months) Suppose the cost of hiring and training a new agent is $1,140. The manager of this call center believes that increasing agents’ salaries would keep them working longer at the company. The manager wants to increase the average time that an agent works for the call center to 36 months, or three years. b-1. Given the current average working time for agents at this call center, determine the current annual cost for hiring and training. b-2. Assuming the average time that an agent works for the call center is increased to 36 months, determine the new annual cost for hiring and training. b-3. If the time an agent works for the call center is increased to 36 months on average, how much could the company save on hiring and training costs over a year?27 In order to manufacture 3,000 pairs of shoes in a week, a firm can use 3,000 workers and 100 machines or 200 machines and 4,000 workers Which method is considered more technically efficient? a 4,000 workers and 200 machines b Both are equally efficient c 3,000 workers and 100 machines d Neither could be considered efficient 33 A manufacturing business can use 100 workers and 20 machines, 140 workers and 18 machines, or 150 workers and 18 machines to produce 80 chairs If each worker costs $40 and each machine is rented for $1000, the economically efficient input combination is: a 100 workers and 20 machines b 150 workers and 18 machines c none of these input combinations d 140 workers and 18 machines
- Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.You are working to model your production function and you are interested in the equation of the line tangent to the production function at a specific level of production. You know that the equation of the tangent line will be first derivative of the production function. Given this information, Previously, a consultant had estimated that your production function could be estimated as f(x) = -1,000 + 26 hours - 0.2 hours^2 Given that you firm is planning to use 97 hours in the production process, what is the value of the equation of the tangent line at 97?Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize f = 20x + 12y + 12z subject to the following. x + z ≤ 45 x + y ≤ 30 y + z ≤ 45 (x,y,z)= f=
- Chemco produces three products: 1, 2, and 3. Eachpound of raw material costs $25. It undergoes processingand yields 3 oz of product 1 and 1 oz of product 2. It costs$1 and takes 2 hours of labor to process each pound of rawmaterial. Each ounce of product 1 can be used in one ofthree ways.It can be sold for $10/oz.It can be processed into 1 oz of product 2. This requires 2 hours of labor and costs $1.It can be processed into 1 oz of product 3. This requires 3 hours of labor and costs $2.Each ounce of product 2 can be used in one of two ways.It can be sold for $20/oz.It can be processed into 1 oz of product 3. This requires 1 hour of labor and costs $6.Product 3 is sold for $30/oz. The maximum number ofounces of each product that can be sold is given in Table 23.A maximum of 25,000 hours of labor are available.Determine how Chemco can maximize profit. TAB LE 23Product Oz1 5,0002 5,0003 3,000Inc. wants to analyze its variances in its actual and budgeted operation. · There is no difference between the actual gross profit and budgeted gross profit.· The quantity of units sold is the same as the budgeted units sold.· Actual Units sold at budgeted sales price is P10,000· Actual Units sold at budgeted cost price is P8,000· Budgeted Sales is at P10,000 and the actual sales is P1,500 greater than the budgeted sales· Budgeted Cost of Goods Sold is at P8,000 and the actual Cost of Goods Sold is P1,200 greater than the budgeted Cost of Goods Sold.What is the sale price variance?You are the district manager for the NCDNR aka the Game Wardens. You staff your law enforcement officers such that they have a 10 hour work day in a single shift. This means that they work 4 days in a row and have 3 consecutive days off. For your district, you need to make sure that you have at least: 10 working on Saturday, 0 on Sunday, 3 on Monday, 3 on Tuesday, 5 on Wednesday, 4 on Thursday, and 8 on Friday. Your current compensation plan approved by the state is: Days off M,T,W T,W,Th W,Th,F Th,F,Sa F,Sa,Su Sa,Su,M Su,M,T Wage 3000 2900 2820 2750 2600 2700 2720 Questions: What is the objective function value? How many employees do you have? How many people show up for work on Sunday, despite this not being necessary according to the scheduling requirements?