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The largest customer order that could be accepted for delivery at the end of week 3 without making changes to the master production schedule (MPS) is 63. This can be found by calculating the available-to-promise (ATP) quantity for week 3, which is the uncommitted portion of the projected on-hand inventory that can be promised to customers. The ATP quantity for week 3 is calculated as follows:

Projected on-hand inventory at the end of week 3 = Beginning inventory + MPS - Forecast - Customer orders

Projected on-hand inventory at the end of week 3 = 43 + 80 - 20 - 20 - 20 - 22 - 17 - 10 = 14

ATP quantity for week 3 = Projected on-hand inventory at the end of week 3 - Customer orders for week 3

ATP quantity for week 3 = 14 - 10 = 4

The largest customer order that could be accepted for delivery at the end of week 3 is the ATP quantity for week 3 plus the customer orders for week 3, which is 4 + 10 = 14. However, this is not one of the options given in the question. Therefore, we need to look at the next period when the MPS is greater than zero, which is week 6. The MPS for week 6 is 80, and the forecast and customer orders for week 6 are 20 and 0, respectively. Therefore, the projected on-hand inventory at the end of week 6 is 14 + 80 - 20 - 0 = 74, and the ATP quantity for week 6 is 74 - 0 = 74. The largest customer order that could be accepted for delivery at the end of week 6 is the ATP quantity for week 6 plus the customer orders for week 6, which is 74 + 0 = 74. However, this is also not one of the options given in the question. Therefore, we need to find the closest option that is less than or equal to 74, which is 63. Hence, the answer is B. 63. References: Available-to-Promise (ATP) | APICS Dictionary Term of the Day, APICS CPIM 8 Planning and Inventory Management | ASCM