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A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with the probabilities: $10 0.9, $50 0.1. Over many weeks, what is a worker's expected weekly bonus?
1. (10 + 50)/2=$30
2. 10 x 0.9 + 50 x 0.1=$14
3. (10 x 0.9 + 50 x 0.1) / 2=$7
4. (10 + 50) / 10= $6
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- The owners of a small manufacturing concern have hired a vice president to run the company with the expectation that he will buy the company after five years. Compensation of the new vice president is a flat salary plus 75% of the first $150,000 profit, and then 10% of profit over $150,000. Purchase price for the company is set at 4.5 times earnings (profit), computed as average annual profitability over the next five years. a.Plot the annual compensation of the vice president as a function of annual profit. b.Assume the company will be worth $10 million in five years. Plot the profit of buying the company as a function of annual profit. c.Does this contract align the incentives of the new vice president with the profitability goals of the owners?The number of hybrid cars that have be requested for rental from a car rental office during a 50 day sample period is given in the following table. Demand for Cars Number of Days Probability 3 3 0.06 4 7 0.14 5 12 0.24 6 14 0.28 7 10 0.20 8 4 0.08 50 1.00What is the expected (mean) number of hybrid rentals per day? Compute to one decimal place.2-41 The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. a. What is the probability the project will be finished in 62 weeks or less? b. What is the probability the project will be finished in 66 weeks or less? c. What is the probability the project will take longer than 65 weeks?
- e) (P1, P2, P3, y1, y2, y3) = (0, 77, 109, 0, 1, 1) with a profit of $ 5260is wrongA company is planning to launch a new product. It currently has four possible new products under consideration to invest in but it must select one. It has estimated the following data: Product Expected annual demand Unit cost of production Unit selling price Fixed cost incurred before production Expected product life in years A 500 Product B Product A Product C Product D £700 £900 £150,000 2 years B 700 £900 £1300 £350,000 2.5 years C 850 £1000 £1400 £450,000 3 years D 1000 £1200 £1500 £550,000 3.25 years On the basis that the main selection criterion is the product that offers the largest safety margin between break even quantity and expected product life select the safest product to invest in.7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran- dom variable with cumulative distribution function F(t) = 1 – e/10 – (1/10) e¯/10 for all t> 0. a. What is the probability density function of T? b. What is the probability that a piece of equipment survives more than 20 years? c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years? d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years? 8. For the equipment mentioned in Problem 7, a. Derive the failure rate function r(1), and draw a graph of the function. b. Without using the failure rate function, determine the probability that a piece of equipment that has survived 20 years of operation fails in the 21st year. c. Does r(20) accurately estimate your answer to part (b)? Why or why not?
- A workshop has 20 nos. of identical machines. The failure pattern of the machine is given below:- Elapsed time after Maintenance attention (in month) 1 2 Probability of failure 3 4 5 6 0.20 0.15 0.15 0.15 0.15 0.20 It costs 150 to attend a failed machine and rectify the same. Compute the yearly cost of servicing the broken down machines.ABC Manufacturing Co. has just observed a job in its laboratory in anticipation of releasing the job to the factory for production. The firm wants rather a good accuracy for costing and labor forecasting. Specifically, it wants to provide a 99% confidence level and a cycle time that is within 2% of the true value. Observation Time 1 1.8 2 1.6 3 1.5 4 1.4 5 1.5 6 1.5When performing sales mix analysis , which one of the following is false : a. Producing and selling more units of the product with a higher contribution margin would likely decrease the breakeven point b. Making changes to the sales mix will likely cause a change in the breakeven point c. The sales mix is usually assumed to be remain the same . d. Shifting the sales mix to the product with a lower contribution margin will likely ncrease the overall contribution margin e. Normally the calculation of the breakeven point for multiproduct is more complicated than that for a single product
- Find the formula for g in terms of f. g(x) = -12 12 2.0 12 2.0 2.0 12 12 2.0 -12 Find the formula for g in terms of f. g(x) = -12Suppose that each engine can be inspected before theflight. After inspection, each engine is labeled as being ineither good or bad condition. You are given thatP(inspection says engine is in good condition | engine willfail) .001P(inspection says engine is in bad condition | engine willfail) .999P(inspection says engine is in good condition | engine willnot fail) .995 P(inspection says engine is in bad condition | engine willnot fail) .005 a If the inspection indicates the engine is in bad con-dition, what is the probability that the engine will fail on the flight?b If an inspector randomly inspects an engine (that is,with probability .001 she chooses an engine that is aboutto fail, and with probability .999 she chooses an enginethat is not about to fail), what is the probability that shewill make an error in her evaluation of the engine?A company installs new central-heating furnaces and has found that for 15% of all installations, a return visit is needed to make some modifications. Six installations were made in a particular week. Assume independence of outcomes for these installations.a. What is the probability that a return visit will be needed in all these cases?b. What is the probability that a return visit will be needed in none of these cases?c. What is the probability that a return visit will be needed in more than 1 of these cases?