Question: Example 2.4 Calculating production quantities that will maximize profit A foundry produces castings to order. An order for 20 custom-designed castings has been received. The

Example 2.4 Calculating production quantities

Example 2.4 Calculating production quantities that will maximize profit A foundry produces castings to order. An order 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 castingsno more, no less! Based on historical records, the probability dis- tributions given in Table 2.6 have been estimated. How many castings should be scheduled 12 13 Table 2.6 Probability Distributions for the Number of Good Castings (x) out of Q # Good Number of Castings Produced Q Castings (x) 20 21 22 23 24 25 26 27 28 29 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 14 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 0.00 16 0.10 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 0.00 17 0.10 0.10 0.05 0.05 0.05 0.05 0.00 0.00 0.00 0.00 18 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.00 0.00 0.00 19 0.20 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.00 0.00 20 0.25 0.20 0.15 0.10 0.10 0.05 0.05 0.05 0.05 0.00 21 0.00 0.25 0.20 0.15 0.10 0.10 0.05 0.05 0.05 0.05 22 0.00 0.00 0.25 0.20 0.15 0.10 0.10 0.05 0.05 0.05 23 0.00 0.00 0.00 0.25 0.20 0.15 0.10 0.10 0.05 0.05 24 0.00 0.00 0.00 0.00 0.25 0.20 0.15 0.10 0.10 0.05 25 0.00 0.00 0.00 0.00 0.00 0.25 0.20 0.15 0.10 0.10 26 0.00 0.00 0.00 0.00 0.00 0.00 0.25 0.20 0.15 0.10 27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25 0.20 0.15 28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25 0.20 29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.25 30 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 30 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.05 0.05 0.10 0.10 0.15 0.20 0.25

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