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2.28 A foundry produces castings to order. An order for 20 special castings has been re- ceived. Since the casting process is highly variable, not all castings produced are good. The cost of producing each casting is $550; the additional cost of finishing a good casting is $125. If a casting is not good, it is recycled at a value of $75; excess good castings are not finished but are recycled at a value of $75. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Prob- ability distributions for the number of good castings produced in a batch of varying sizes are given below. How many castings should be scheduled in order to maximize expected profit?

2.28 A foundry produces castings to order. An order for 20 special castings has been re- ceived. Since the casting process is highly variable, not all castings produced are good. The cost of producing each casting is $550; the additional cost of finishing a good casting is $125. If a casting is not good, it is recycled at a value of $75; excess good castings are not finished but are recycled at a value of $75. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Prob- ability distributions for the number of good castings produced in a batch of varying sizes are given below. How many castings should be scheduled in order to maximize expected profit?

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2.28 A foundry produces castings to order. An order for 20 special castings has been re- ceived. Since the casting process is highly variable, not all castings produced are good. The cost of producing each casting is $550; the additional cost of finishing a good casting is $125. If a casting is not good, it is recycled at a value of $75; excess good castings are not finished but are recycled at a value of $75. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Prob- ability distributions for the number of good castings produced in a batch of varying sizes are given below. How many castings should be scheduled in order to maximize expected profit? #Good Castings 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 79 2 PRODUCT, PROCESS, AND SCHEDULE DESIGN Number of Castings Scheduled 15 16 17 0.05 0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.00 0.00 0.00 0.00 0.05 0.05 0.05 0.00 0.00 0.00 0.05 0.05 0.05 0.05 0.00 0.00 0.05 0.05 0.05 0.05 0.05 0.00 0.05 0.05 0.05 0.05 0.05 0.05 0.10 0.05 0.05 0.05 0.05 0.05 0.05 22 23 24 25 26 27 28 29 30 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 18 19 20 21
Transcribed Image Text:2.28 A foundry produces castings to order. An order for 20 special castings has been re- ceived. Since the casting process is highly variable, not all castings produced are good. The cost of producing each casting is $550; the additional cost of finishing a good casting is $125. If a casting is not good, it is recycled at a value of $75; excess good castings are not finished but are recycled at a value of $75. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Prob- ability distributions for the number of good castings produced in a batch of varying sizes are given below. How many castings should be scheduled in order to maximize expected profit? #Good Castings 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 79 2 PRODUCT, PROCESS, AND SCHEDULE DESIGN Number of Castings Scheduled 15 16 17 0.05 0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.00 0.00 0.00 0.00 0.05 0.05 0.05 0.00 0.00 0.00 0.05 0.05 0.05 0.05 0.00 0.00 0.05 0.05 0.05 0.05 0.05 0.00 0.05 0.05 0.05 0.05 0.05 0.05 0.10 0.05 0.05 0.05 0.05 0.05 0.05 22 23 24 25 26 27 28 29 30 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 18 19 20 21
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