Problem
The company CALDIS Ltd produces boxes of Christmas candies that are sold to a chain of stores. The company wants to prepare its stock of candy boxes for this winter knowing that it has a production cost of 32 RON per box. The company knows that for the orders received until the end of the year, it will receive an average price of 62 RON per box. Concerning the remaining stock, the company knows it can sell it at the beginning of next year for only 30 RON/box to a seller in the market due to the winter discount period at the beginning of the new year. The company also knows that for each candy box requested and not provided, the stores penalize it with 10 RON per box. From past sales of Christmas candies boxes, the manager estimates the demands for the current year and the corresponding probabilities of occurrence presented in the table. Calculate the expected profits and indicate the optimal supply quantity this year.