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3) (10 points) A foundry has received an order for 3-4 custom designed castings. The casting process costs $800 per unit scheduled. The customer has indicated willingness to pay $2003 shown in the table below have been estimated. How many castings should be scheduled for fewer than 3 or more than 4 castings. Based on historical data, the probability distributions castings is made? What is the probability of losing money when this number of castings is production to maximize expected profit? What is the expected profit when this number of made? 0.00 #good castings 3 0 0.20 1 0.30 2 0.30 3 0.20 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 Number of Castings Scheduled 8 4 5 7 6 0.05 0.00 0.00 0.00 0.20 0.10 0.05 0.00 0.00 0.25 0.20 0.15 0.10 0.05 0.25 0.20 0.15 0.10 0.25 0.20 0.20 0.15 0.00 0.20 0.20 0.20 0.00 0.00 0.20 0.20 0.20 0.00 0.00 0.15 0.15 0.00 0.00 0.00 0.15 0.30 0.20 0.20 0.00 0.00