A foundry produces castings to order. An order for 20 special castings has been received. Since the casting process is highly variable, not all casting 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 $100. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1,250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Derive a function of expected profit. The probability of a casting meeting the final inspection standard to be good is 0.80. Determine the number of casts to be scheduled for production to maximize expected profit, and estimate the probability of losing money. Hint: use Excel.