a. What is the probability that you receive a non-defective connector? b. You buy one of these components and find that it is defective. What is the probability that your component came from supplier A?
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![A company manufacturing electronic components for home entertainment systems buys
electrical connectors from three suppliers. The company prefers to use supplier A because only
1% of those connectors are defective, but supplier A can only deliver 70% of the connectors
needed. The company must also purchase connectors from two other suppliers: 20% are from
supplier B, and the rest from supplier C. The rate of defective connectors from B is 2%, and the
rate from C is 4%.
a. What is the probability that you receive a non-defective connector?
b. You buy one of these components and find that it is defective. What is the probability
that your component came from supplier A?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b3925e9-3698-4de9-9f01-eff4f69c62e5%2F64a2a93f-034a-4a2f-9a6c-50643d97233c%2Frtkp74r_processed.png&w=3840&q=75)
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- You're a quality engineer at Norman's fouth largest cracker factory. where there are two production lines (A, which produces 20% of cracker boxes, and B which produces the rest). If a line produces more than one defective box in an eight -hour day, a maintenance check on the line is performed. Line A produces an average of 0.061 box defects PER Hour. Given that you're only looking at a line A, what is the probability that you will need a request a maitenance check.A manufacturing company is analyzing its accident record. The accidents fall into two categories: Minor—dealt with by first aider: Average cost k50 Major—hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. [] On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.A manufacturing company is analyzing its accident record. The accidents fall into two categories: Minor—dealt with by first aider: Average cost k50 Major—hospital required. Average cost k1,000The company has 1,000 employees, of which 180 are office staff and the rest work in the factory.The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year.(i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii)Show that the probability that a given a member of office staff has an accident in a year is 0.0549.(iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.
- A manufacturing company is analyzing its accident record. The accidents fall intotwo categories: Minor—dealt with by first aider: Average cost k50 Major—hospital required. Average cost k1,000The company has 1,000 employees, of which 180 are office staff and the restwork in the factory.The analysis shows that 10% of employees have an accident each year and 20%of accidents are major. It is assumed that an employee has more than oneaccident in a year.(i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half theprobability of having an accident relative those in the factory.(ii)Show that the probability that a given a member of office staff has anaccident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has hadan accident is office staffConsider a person who invests in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 6.5% on AAA bonds, 7% on A bonds, and 9% on B bonds. The person invests twice as much in B bonds as in A bonds. Let x, y and z represent the amounts invested in AAA, A, and B bonds, respectively. x + y + z = 10,000(total investment) 0.065x + 0.07y + 0.09z = 760(annual return) 2y – z = 0 Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond. Total Investment Annual Return $10,000 760A student received an A- in Engineering Math (3 credits), a B+ in introduction to PDT ( 3 credits), an B in Client server ( 3 credits), and a A in Technical writing ( 2 credits). Assuming that, A = 4 grade points, A- = 3.7 grade points, B+ = 3.3 grade points, B = 3 grade %3D %3D points, B- = 2.7 grade points, and C+ = 2.3 grade point, C = 2 %3D grade points and C- = 1.7 grade points. Find the student's grade point average (GPA)? [2 decimal place calculation] O a. 7.37 b. 3.37 О с. 3.73 d. None of the option is correct
- A company needs to rent space for its office employees both in the suburbs and downtown. Space is available in suburbia at a rate of $120 per square metre (per annum), while downtown space rents for $250 per square metre (per annum). In suburbia, only 30% of the space is “executive” quality, while the rest is ordinary quality. At the downtown location, 70% of the space is executive quality, while the rest is ordinary quality. The company needs a total of at least 1000 square metres of space, of which at least 510 square metres must be executive quality. No more than three quarters of the entire space is to be at either location. They wish to know how much space they should rent in each place so as to minimize the total expenditure on rent. a) Show the decision variables b) Show the objective function c) Show the constraints in standard form (i.e. suitable for using Excel’s Solver) d) Solve the linear programming problem by graphingA diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?California Wine producer Chill Wines has in their line a mid-market chardonnay, of whichthey produce 200,000 bottles a year. They have been bottling their wines with natural corkclosures, which are known to have sealing issues resulting in the spoilage of wine, aproblem that is worse in their chardonnay than in the other wines they sell. This problem,which results in a 15% spoilage rate for their chardonnay, is both expensive and impactsthe company’s reputation. They have researched several other closure products on themarket and have decided to try using a new closure in a test run of 91 bottles theirchardonnay. After allowing the wine to stay in the bottles for the time it generally takes toget it from the winery to customers, they tested the run and found 16 spoiled bottles. As thecompany has a both an immediate financial and reputation risk, they want to be 90% surethat changing the closures will help limit wine spoilage. What do their results suggest? a)What is known? What…
- A farmer has recently acquired a 110 hectares piece of land. He has decided to grow Wheat and barley on that land. Due to the quality of the sun and the region's excellent climate, the entire production of Wheat and Barley can be sold. He wants to know how to plant each variety in the 110 hectares, given the costs, net profits and labor requirements according to the data shown below: Variety Cost (Price/Hec) Net Profit (Price/Hec) Man-days/Hec Wheat 100 50 10 Barley 200 120 30 The farmer has a budget of US$10,000 and an availability of 1,200 man-days during the planning horizon. In addition, the farmer would like to get a profit of at least $3000. Generate the mathematical model for the optimal usage of land area to produce wheat and barley. Using graphical method to optimize land usage, how many hectares are to be used for wheat and barley.Zelle's Dry Cleaners has collected the following data for its processing of dress shirts: It takes an average of 3,5 hours to dry clean and press a dress shirt, with value-added time estimated at 110 minutes per shirt. Workers are paid for a 7-hour workday and work 5,5 hours per day on average, accounting for breaks and lunch; labor utilization is 75 percent in the industry. The dry cleaner completes 25 shirts per day, with an industry standard of 28 shirts per day for a comparable facility. Determine process velocity, labor utilization, and efficiency for the company.Workers at a particular mining site receive an average of 35 days paid vacation, which is lower than the national average. The manager of this plant is under pressure from a local union to increase the amount of paid time off. However, he does not want to give more days off to the workers because that would be costly. Instead he decides he should fire 10 employees in such a way as to raise the average number of days off that are reported by his employees. In order to achieve this goal, should he fire employees who have the most number of days off, least number of days off, or those who have about the average number of days off? a. He should fire employees who have the most number of days off. b. No matter who he fires, it will not increase the amount of paid time off. c. He should fire employees who have the average number of days off. d. He should fire employees who have the least number of days off.
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