Carefully study Example 2.4 in the text, and answer the following questions:

Verify that the columns in Table 2.6 sum to 1.00. What does this mean?

Calculate the revenue and costs that would result if 20 castings are ordered, but only 12 are good. Verify that the profit number given in Table 2.7 for this scenario is correct.

Calculate the revenue and costs that would result if 24 castings are ordered, and 20 good castings are produced. Verify that the profit number given in Table 2.7 for this scenario is correct.

Verify that the expected profit from ordering 21 castings is $1800.

Example 2.4 Calculating production quantities that will maximize profit A foundry produces castings to order. An onder for 20 custom-designed castings has been received. The casting process costs $1100 per unit scheduled. If a casting is not sold, it has a recycle value of $200. The customer has indicated a willingness to pay $2500 per casting for 20 acceptable castings-no more, no less! Based on historical records, the probability dis- tributions given in Table 2.6 have been estimated. How many castings shoud be scheduled Table 2.6 Probbility Distribntions for tbe Number of Good Castings (x)out of O Good Number of Castings Produced0) 021 22 23 24252627282 30 12 0.05 000 000 0.00 000 0000.00 0.00 000 0.00 000 3 0.05 0.05 0.000.00 000 0.00 0.00 0.00 0.00 0.00 0.00 40.05 0.05 005 0.00 0.00 0.00 0.00 0.00 000 0.00 0.00 5 0.05 005 005 0.05 0.00 0.00 0.00 0.00 000 0.00 0.00 6 0.10 0.05 005 0.050. 000 0.00 0.00 0.00 0. 0.00 17 0 10 0.10 005 0.05 005 05 0.00 0.00 000 0.00 0.0 18 0.15 0.10 0.10 0.05 0 00 0.05 0.00 0.000. 0.00 9 0.20 0.15 0.10 0.10 0.05 005 0.05 0.00 000 0.0 20 |0.25 0.20 0.15 0.10 0.10 0.05 0.05 0.05 0.05 000 0.00 21 |0.00 0.25 020 0.15 0.10 0.10 0.05 ().05 0.05 0.05 0.00 22 0.00 0.00 0.25 0.2005 0.10 0.10 005 0.0505 005 23 |0.00 000 000 0,25 020 0,15 0,10 010 005 O.05 005 24 0.00 0.00 0.00 0.00 0.25 0.20 0.1500.10 005 0.0 25 0.00 0.00 0.00 0.00 0.00 0.25 0.205 0.10 0.10 0.0 26 0.00 0.00 0.00 0.00 0.00 000 0.25 0.20 0.15010 0.10 7 0.00 0.00 0.00 0.00.0 000 0.00 025 0.20 015 0.10 280.00 0.00 0.000.00 000 0.00 0.00 0.00 0.250.20 0.15 2 0.00 0.00 0.000.00 000 0.00 0.00 0.00 0.00 0.25 0.20 0 0.00 0.00 000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25