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Daily demand for a type of sandwich sold at Door Red Cafe (DRC) is normally distributed with a mean of 65 and a standard deviation

Daily demand for a type of sandwich sold at Door Red Cafe (DRC) is normally distributed with a mean of 65 and a standard deviation of 27. DRC orders the sandwiches from a wholesaler (everyday morning before 5:30 AM) at a wholesale price of $4 per sandwich and sells them at a retail price of $7 per sandwich. Pursuant to the contract between DRC and its wholesaler, the transportation cost is currently borne by the wholesaler. The wholesaler does not take back any unsold sandwiches. However, DRC can sell any unsold inventory at a discounted price of $3 after 5:00 PM every day.

Now suppose that the contract between DRC and its wholesaler expires and pursuant to the new contract, if DRC orders more than 56 sandwiches (anything more than or equal to 57), the transportation cost is no longer borne by the wholesaler and DRC will have to pay $30 for transportation. If DRC orders less than or equal to 56, the transportation cost for DRC is still zero. What is DRC's optimal order quantity for this type of sandwich now?

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