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Question 2. Sweetie, a chocolate manufacturer, produces heart shaped chocolates for Valentine's Day. A102 makes a single order decision at the end of January every
Question 2. Sweetie, a chocolate manufacturer, produces heart shaped chocolates for Valentine's Day. A102 makes a single order decision at the end of January every year for that year's Valentine's Day. The retail price for the chocolate is $18. Sweetie charges A102$14 for the chocolate and incurs a production cost of $10. A stock-out situation at A102 results in $9 and at Sweetie $12 per unit. Both Sweetie and A102 can sell an unsold chocolate to a 3rd party for $6 per unit. a) Write the profit function of A102 for a given realization of demand (hint: PA(Qx) ). b) Write the expected profit function of A102 (hint: E[PA(Q)]). c) Write the profit function of Sweetie for a given realization of demand. d) Write the expected profit function of Sweetie. e) What are the costs of overage and underage for A102? f) Assume that demand for chocolates is uniformly distributed between 1000 and 2500 . What is the optimal order size of A102? g) Calculate the optimal expected profits of the parties under the uniformly distributed demand assumption. h) Assume that demand for chocolates is normally distributed with mean 1500 and variance 900 . What is the optimal order size of A102? i) Assume that demand for chocolates is exponentially distributed with mean 1500 . What is the optimal order size of A102? Suppose that Sweetie changed its current policy and allow A102 to return 20% of his initial purchase for $8 and order quantity of A102 is 1000 . j) Write the profit function of A102 for a given realization of demand. k) Write the expected profit function of A102. 1) Write the profit function of Sweetie for a given realization of demand. m) Write the expected profit function of Sweetie. n) Is this return policy optimal? Why or why not? What should the optimal policy satisfy
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