For the basic age replacement model, consider a piece of equipment that costs$18,000 to replace. The total maintenance costs for five years of operation areestimated to be $2,400. Assuming a linear maintenance cost rate, find the value ofa and the optimal age at which the equipment should be replaced.
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For the basic age replacement model, consider a piece of equipment that costs
$18,000 to replace. The total maintenance costs for five years of operation are
estimated to be $2,400. Assuming a linear maintenance cost rate, find the value of
a and the optimal age at which the equipment should be replaced.
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Long-Life Insurance developed a linear model to determine the amount of term life insurance a family of four should have, based on the head of the household's current age. The equation is: y = 163 -0.45xwherey = Insurance needed ($000)x = Current age of head of household Calculate the amount of term life insurance you would recommend for a family of four if the head of the household is 53 years old. (Round your answer to 2 decimal places.)What is an example of a learning objective for a lesson on Integrating Writing in Math in a first-grade classroom? The learning objective should include the following required components: behavior, condition, and measurable criterion that aligns with both of the below standards. Math Standard Solve real-world problems involving addition and subtraction within 20 in situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all parts of the addition or subtraction problem (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Writing Standard Produce (when writing or speaking) a topic sentence or main idea, provide some facts or details about the topic, and provide a concluding statement.
- As the Quality Sweaters problem is now modeled, if all inputs remain fixed except for the number mailed, profit will increase indefinitely as the number mailed increases. This hardly seems realistic—the company could becomeinfinitely rich. Discuss realistic ways to modify the model so that this unrealistic behavior is eliminated.A company has determined that its profit for a product can be described by a linear function.The profit from the production and sale of 150 units is $455, and the profit from250 units is $895.(b) You are the CEO for a lightweight compasses manufacturer. The demandfunction for the lightweight compasses is given by p = 40 − 4q2where qis the number of lightweight compasses produced in millions.It costs the company $15to make a lightweight compass.(i) Write an equation giving profit as a function of the number of lightweight compassesproduced.(ii) At the moment the company produces 2 million lightweight compasses and makes a profitof $18,000,000, but you would like to reduce production. What smaller number oflightweight compasses could the company produce to yield the same profit?A borrower takes out a 30-year adjustable rate mortgage loan for $200,000 with monthly payments. The first two years of the loan have a "teaser" rate of 4 percent, after that the rate can reset with a 5 percent annual payment cap. On the reset date, the composite rate is 6 percent. Assume that the loan allows for negative amortization. What would be the outstanding balance on the loan at the end of Year 3? Multiple Choice $192,926 $190,074 $192,812 $192,337
- Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand is $50.00. Her best guess is that she can sell 300 cups per week at $0.50 per cup. The variable cost of producing a cup oflemonade is $0.20.a. Given her other assumptions, what level of sales volume will enable Julie to break even?b. Given her other assumptions, discuss how a change in sales volume affects profit.c. Given her other assumptions, discuss how a change in sales volume and variable cost jointly affect profit.d. Use Excel’s Formula Auditing tools to show which cells in your spreadsheet affect profit directly.You are the manager of GearNet and must decide how many Internet hubs to produce to maximize your firm’s profit. GearNet and its only rival (NetWorks) sell dual-speed Internet hubs that are identical from consumers’ perspectives. The market price for hubs depends on the total quantity produced by the two firms. A survey reveals that the market price of the hubs depends on total market output as follows: Combined Hub Production of GearNet and NetWorks Market Price of Hubs (per unit) 500 units $120 750 units $100 1,000 units $90 GearNet and NetWorks each use labor, materials, and machines to produce output. GearNet purchases labor and materials on an as-needed basis; its machines were purchased three years ago and are being depreciated according to the straight-line method. GearNet’s accounting department has provided the following data about its unit production costs: Item GearNet’s Unit Cost for an Output of: 250 units…The IRR is the discount rate r that makes a project have an NPV of 0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function might not find an answer, and you would get an error message. Then you must try the syntax =IRR(range of cash flows, guess), where guess" is your best guess for the IRR. It is best to try a range of guesses (say, 90% to 100%). Find the IRR of the project described in Problem 34. 34. Consider a project with the following cash flows: year 1, 400; year 2, 200; year 3, 600; year 4, 900; year 5, 1000; year 6, 250; year 7, 230. Assume a discount rate of 15% per year. a. Find the projects NPV if cash flows occur at the ends of the respective years. b. Find the projects NPV if cash flows occur at the beginnings of the respective years. c. Find the projects NPV if cash flows occur at the middles of the respective years.
- Assume that all of a companys job applicants must take a test, and that the scores on this test are normally distributed. The selection ratio is the cutoff point used by the company in its hiring process. For example, a selection ratio of 25% means that the company will accept applicants for jobs who rank in the top 25% of all applicants. If the company chooses a selection ratio of 25%, the average test score of those selected will be 1.27 standard deviations above average. Use simulation to verify this fact, proceeding as follows. a. Show that if the company wants to accept only the top 25% of all applicants, it should accept applicants whose test scores are at least 0.674 standard deviation above average. (No simulation is required here. Just use the appropriate Excel normal function.) b. Now generate 1000 test scores from a normal distribution with mean 0 and standard deviation 1. The average test score of those selected is the average of the scores that are at least 0.674. To determine this, use Excels DAVERAGE function. To do so, put the heading Score in cell A3, generate the 1000 test scores in the range A4:A1003, and name the range A3:A1003 Data. In cells C3 and C4, enter the labels Score and 0.674. (The range C3:C4 is called the criterion range.) Then calculate the average of all applicants who will be hired by entering the formula =DAVERAGE(Data, "Score", C3:C4) in any cell. This average should be close to the theoretical average, 1.27. This formula works as follows. Excel finds all observations in the Data range that satisfy the criterion described in the range C3:C4 (Score0.674). Then it averages the values in the Score column (the second argument of DAVERAGE) corresponding to these entries. See online help for more about Excels database D functions. c. What information would the company need to determine an optimal selection ratio? How could it determine the optimal selection ratio?Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of 150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of 250 per room. a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100. b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?In Example 11.3, if a batch fails to pass inspection, the entire batch is unusable. Change the model so that if a batch fails to pass inspection, it is reworked, and at the end of the rework, its entire yield (the same yield determined in column C) is usable. However, the rework takes 3, 4, or 5 days with respective probabilities 0.2, 0.5, and 0.3. Run the simulation for the modified model and comment on how the results change.