Question 1 8 pts Problem 638608: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Samsung manufactures cellular phones at a processing cost of $202 per unit. Currently, the company produces an average of 2011 phones per day, 90 percent of which are good-quality phones, resulting in 10 percent defective phones, 64 percent of which can be reworked. The cost of reworking a defective phone is $74. They also consider a quality improvement initiative: They can replace a plastic component with a metal one which increases the initial cost of processing phone to $207, but the percentage of defective items decreases to 3 percent. With this quality improvement option, nothing else would be different from the current situation (for example the cost of rework and the percentage of defectives that can be reworked stay the same). Calculate the followings: Number of units reworked daily with current situation: Daily product yield with current situation: Effective production cost per unit with current situation: With the current situation, if the company wants the yield to be 2000, how many phones should they process daily? Number of units reworked daily with suggested quality improvement option: Daily product yield with suggested quality improvement option: Effective production cost per with suggested quality improvement option: Should Samsung should take the suggested quality improvement initiative? (Yes/No) Question 2 4 pts Problem 775702: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Zed and Adrian and run a small bicycle shop called "Z to A Bicycles". They must order bicycles for the coming season. Zed and Adrian estimate that the demand for bicycles this season will be 20, 30, 40, or 50 bicycles with probabilities of 0.2, 0.4, 0.3, and 0.1 respectively. Orders for the bicycles must be placed in quantities of twenty (20). The cost per bicycle is $70 if they order 20, $60 if they order 40, $52 if they order 60. The bicycles will be sold for $76 each if they are not on sale. Any bicycles left over at the end of the season will go on sale and will be sold at $46 each. Create a payoff table that helps Z to A Bicycle decide how many bicycles (20, 40, or 60) to order. Complete the Following Payoff Table: Demand=20 Demand=30 Demand=40 Demand=50 ... ... Order20 Order40 Order 60 ... Question 3 10 pts Problem 188109: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed, so that no company knows what the others are bidding, and the low bid wins the contract. SciTools estimates that it will cost $95k to supply the instruments if it wins the contract. The company is deciding to bid against the competitors. On the basis of past contracts of this type, SciTools believes that the competitors' bids are based on the following probabilities and they have created the payoff table as follows. Probability 0.35 0.05 0.6 Competitors' lowest bid is between $110k and $125k between $125k and $135kmore than $135k bid 110k (low) 15k 15k 15k bid 125k (medium) 0 30k 30k bid 135k (high) 0 0 40k Note: You can drop 3 zeros for numbers in thousands. How much in thousands) is the expected payoff if the company bids low? How much (in thousands) is the expected payoff if the company bids medium? How much in thousands) is the expected payoff if the company bids high? What is the best decision based on expected value approach? (Bid Low/Bid Medium/Bid High) How much in thousands) is the expected payoff if the company has full information about competitors' bid? Calculate the expected value of perfect information (in thousands)? How much (in thousands) is the maximum regret of the company if they bid low? How much in thousands) is the maximum regret of the company if they bid medium? How much (in thousands) is the maximum regret of the company if they bid high? What is the best decision based on minimax regret approach? (Bid Low/Bid Medium/Bid High) Question 4 6 pts Problem 690710: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed, so that no company knows what the others are bidding, and the low bid wins the contract. SciTools estimates that it will cost $95k to supply the instruments if it wins the contract. The company is deciding to bid against the competitors. On the basis of past contracts of this type, SciTools believes that the competitors' bids are based on the following probabilities and they have created the payoff table as follows. Probability 0.35 0.05 0.6 Competitors' lowest bid is between $110k and $125k between $125k and $135k more than $135k bid 110k (low) 15k 15k 15k bid 125k (medium) 0 30k 30k bid 135k (high) 0 0 40k Note: You may drop 3 zeros of thousand numbers. What is the best decision based on optimistic approach? (Bid Low/Bid Medium/Bid High) What is the best decision based on pessimistic approach? (Bid Low/Bid Medium/Bid High) How much (in thousands) is the average payoff if the company bids low? How much (in thousands) is the average payoff if the company bids medium? How much (in thousands) is the average payoff if the company bids high? What is the best decision based on equal likelihood approach? (Bid Low/Bid Medium/Bid High) Question 5 9 pts Problem 650204: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats at its plant in New England. Wooden bats produced for the mass market are turned on a lathe, where a piece of wood is shaped into a bat with a handle and barrel. The bat is cut to its specified length and then finished in subsequent processes. A specific style of wooden bat is supposed to have a mean barrel circumference of 9 inches with 0.5 inches tolerance at its thickest point. The company is trying to buy a new machine to cut the bats due to a projected increase in sales. There are three different candidate machines that the company is trying to buy at different costs. The following table summarizes the process average, process standard deviation (SD), and purchase cost of each machine. Which machine, if any, should the company purchase (they are trying to buy the cheapest machine that can get the job done)? Machine Average SD Purchase Cost 1 9.17 0.14 $20,000 2 8.99 0.14 $18,000 9.01 0.14 $15,000 Determine the Upper Specification Limit: Determine the Lower Specification Limit: Calculate the process capability index of machine 1: Based on process capability index of machine 1, is machine 1 capable? (Yes/No) Calculate the process capability index of machine 2: Based on process capability index of machine 2, is machine 2 capable? (Yes/No) Calculate the process capability index of machine 3: Based on process capability index of machine 3, is machine 3 capable? (Yes/No) Which machine should the company purchase? (Machine 1/Machine 2/Machine 3/None) Question 6 6 pts Problem 345408: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. An accounts department is concerned about the number of internal purchase forms that its users completed incorrectly. As a result they are monitoring the proportion of purchase forms that were not completed correctly. This was chosen, rather than measuring the actual number of defects, because any number of defects on a form required about the same effort to revise. The following table shows number of forms completed incorrectly "out of 200 forms" that is processed each day. Construct a control chart for the data that monitors the proportion of incorrect forms. Is the process in control? Day 1 Number of Incorrect Forms 17 19 2 3 15 4 17 23 5 6 7 8 15 18 9 15 18 15 10 Sum 172 IMPORTANT: In this problem, keep 3 decimal places in your calculations. Which of the following charts is appropriate? (P Chart/C Chart) Based on your choice on the last question, calculate "one" of the followings, P (for P chart), or C (for C chart): If you chose P Chart, how much is standard deviation of p (sigma_p)? (Write 0 if you are not doing P chart) Upper Control Limit: Lower Control Limit: Is the proportion of incorrect forms in control? (Yes/No) Question 7 10 pts Problem 705203: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Assume you are working in a plant as a chemical engineer. One of your tasks is to monitor pH of a specific process. Each day, you record the pH of process at three different time of the day. The data for the past few days is presented in the following table. we know that standard deviation of the pH of the process is 0.1. Based on the collected data, construct two control charts that monitor the average and variability of the pH of the process. Is the average and variability of the process in control? Recorded pHs: Day 10am 2pm 5pm Monday 7.9 7.02 7.55 Tuesday 7.85 7.997.98 Wednesday 7.37 7.23 7.43 Thursday 7.69 7.22 7.6 Calculate the center line to control the average of pH of the process: Calculate the average of ranges to control the variability of pH of the process: Number of observation in each sample (n): D4: Upper Control Limit to control average of the pH of the process: Lower Control Limit to control average of the pH of the process: Is the average of the pH of the process in control? (Yes/No) Upper Control Limit to control variability of the pH of the process: Lower Control Limit to control variability of the pH of the process: Is the variability of the pH of the process in control? (Yes/No) Question 1 8 pts Problem 638608: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Samsung manufactures cellular phones at a processing cost of $202 per unit. Currently, the company produces an average of 2011 phones per day, 90 percent of which are good-quality phones, resulting in 10 percent defective phones, 64 percent of which can be reworked. The cost of reworking a defective phone is $74. They also consider a quality improvement initiative: They can replace a plastic component with a metal one which increases the initial cost of processing phone to $207, but the percentage of defective items decreases to 3 percent. With this quality improvement option, nothing else would be different from the current situation (for example the cost of rework and the percentage of defectives that can be reworked stay the same). Calculate the followings: Number of units reworked daily with current situation: Daily product yield with current situation: Effective production cost per unit with current situation: With the current situation, if the company wants the yield to be 2000, how many phones should they process daily? Number of units reworked daily with suggested quality improvement option: Daily product yield with suggested quality improvement option: Effective production cost per with suggested quality improvement option: Should Samsung should take the suggested quality improvement initiative? (Yes/No) Question 2 4 pts Problem 775702: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Zed and Adrian and run a small bicycle shop called "Z to A Bicycles". They must order bicycles for the coming season. Zed and Adrian estimate that the demand for bicycles this season will be 20, 30, 40, or 50 bicycles with probabilities of 0.2, 0.4, 0.3, and 0.1 respectively. Orders for the bicycles must be placed in quantities of twenty (20). The cost per bicycle is $70 if they order 20, $60 if they order 40, $52 if they order 60. The bicycles will be sold for $76 each if they are not on sale. Any bicycles left over at the end of the season will go on sale and will be sold at $46 each. Create a payoff table that helps Z to A Bicycle decide how many bicycles (20, 40, or 60) to order. Complete the Following Payoff Table: Demand=20 Demand=30 Demand=40 Demand=50 ... ... Order20 Order40 Order 60 ... Question 3 10 pts Problem 188109: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed, so that no company knows what the others are bidding, and the low bid wins the contract. SciTools estimates that it will cost $95k to supply the instruments if it wins the contract. The company is deciding to bid against the competitors. On the basis of past contracts of this type, SciTools believes that the competitors' bids are based on the following probabilities and they have created the payoff table as follows. Probability 0.35 0.05 0.6 Competitors' lowest bid is between $110k and $125k between $125k and $135kmore than $135k bid 110k (low) 15k 15k 15k bid 125k (medium) 0 30k 30k bid 135k (high) 0 0 40k Note: You can drop 3 zeros for numbers in thousands. How much in thousands) is the expected payoff if the company bids low? How much (in thousands) is the expected payoff if the company bids medium? How much in thousands) is the expected payoff if the company bids high? What is the best decision based on expected value approach? (Bid Low/Bid Medium/Bid High) How much in thousands) is the expected payoff if the company has full information about competitors' bid? Calculate the expected value of perfect information (in thousands)? How much (in thousands) is the maximum regret of the company if they bid low? How much in thousands) is the maximum regret of the company if they bid medium? How much (in thousands) is the maximum regret of the company if they bid high? What is the best decision based on minimax regret approach? (Bid Low/Bid Medium/Bid High) Question 4 6 pts Problem 690710: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed, so that no company knows what the others are bidding, and the low bid wins the contract. SciTools estimates that it will cost $95k to supply the instruments if it wins the contract. The company is deciding to bid against the competitors. On the basis of past contracts of this type, SciTools believes that the competitors' bids are based on the following probabilities and they have created the payoff table as follows. Probability 0.35 0.05 0.6 Competitors' lowest bid is between $110k and $125k between $125k and $135k more than $135k bid 110k (low) 15k 15k 15k bid 125k (medium) 0 30k 30k bid 135k (high) 0 0 40k Note: You may drop 3 zeros of thousand numbers. What is the best decision based on optimistic approach? (Bid Low/Bid Medium/Bid High) What is the best decision based on pessimistic approach? (Bid Low/Bid Medium/Bid High) How much (in thousands) is the average payoff if the company bids low? How much (in thousands) is the average payoff if the company bids medium? How much (in thousands) is the average payoff if the company bids high? What is the best decision based on equal likelihood approach? (Bid Low/Bid Medium/Bid High) Question 5 9 pts Problem 650204: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats at its plant in New England. Wooden bats produced for the mass market are turned on a lathe, where a piece of wood is shaped into a bat with a handle and barrel. The bat is cut to its specified length and then finished in subsequent processes. A specific style of wooden bat is supposed to have a mean barrel circumference of 9 inches with 0.5 inches tolerance at its thickest point. The company is trying to buy a new machine to cut the bats due to a projected increase in sales. There are three different candidate machines that the company is trying to buy at different costs. The following table summarizes the process average, process standard deviation (SD), and purchase cost of each machine. Which machine, if any, should the company purchase (they are trying to buy the cheapest machine that can get the job done)? Machine Average SD Purchase Cost 1 9.17 0.14 $20,000 2 8.99 0.14 $18,000 9.01 0.14 $15,000 Determine the Upper Specification Limit: Determine the Lower Specification Limit: Calculate the process capability index of machine 1: Based on process capability index of machine 1, is machine 1 capable? (Yes/No) Calculate the process capability index of machine 2: Based on process capability index of machine 2, is machine 2 capable? (Yes/No) Calculate the process capability index of machine 3: Based on process capability index of machine 3, is machine 3 capable? (Yes/No) Which machine should the company purchase? (Machine 1/Machine 2/Machine 3/None) Question 6 6 pts Problem 345408: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. An accounts department is concerned about the number of internal purchase forms that its users completed incorrectly. As a result they are monitoring the proportion of purchase forms that were not completed correctly. This was chosen, rather than measuring the actual number of defects, because any number of defects on a form required about the same effort to revise. The following table shows number of forms completed incorrectly "out of 200 forms" that is processed each day. Construct a control chart for the data that monitors the proportion of incorrect forms. Is the process in control? Day 1 Number of Incorrect Forms 17 19 2 3 15 4 17 23 5 6 7 8 15 18 9 15 18 15 10 Sum 172 IMPORTANT: In this problem, keep 3 decimal places in your calculations. Which of the following charts is appropriate? (P Chart/C Chart) Based on your choice on the last question, calculate "one" of the followings, P (for P chart), or C (for C chart): If you chose P Chart, how much is standard deviation of p (sigma_p)? (Write 0 if you are not doing P chart) Upper Control Limit: Lower Control Limit: Is the proportion of incorrect forms in control? (Yes/No) Question 7 10 pts Problem 705203: Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1. Assume you are working in a plant as a chemical engineer. One of your tasks is to monitor pH of a specific process. Each day, you record the pH of process at three different time of the day. The data for the past few days is presented in the following table. we know that standard deviation of the pH of the process is 0.1. Based on the collected data, construct two control charts that monitor the average and variability of the pH of the process. Is the average and variability of the process in control? Recorded pHs: Day 10am 2pm 5pm Monday 7.9 7.02 7.55 Tuesday 7.85 7.997.98 Wednesday 7.37 7.23 7.43 Thursday 7.69 7.22 7.6 Calculate the center line to control the average of pH of the process: Calculate the average of ranges to control the variability of pH of the process: Number of observation in each sample (n): D4: Upper Control Limit to control average of the pH of the process: Lower Control Limit to control average of the pH of the process: Is the average of the pH of the process in control? (Yes/No) Upper Control Limit to control variability of the pH of the process: Lower Control Limit to control variability of the pH of the process: Is the variability of the pH of the process in control? (Yes/No)