Problem 1: Charlie Sells Out (30 points) Charlie Kelly has begun producing and marketing a product called Kitten Mittons, which he buys, sells, and stores in inventory in crates, with each crate hold 50 pairs of Kitten Mittons. Table 1 summarizes the prices at which Kitten Mittons will sell over the following twelve months. At the beginning of each month, Charlie can place an order for up to 20 crates of Kitten Mittons, which cost $30 each and are delivered to him immediately. He can sell these crates of Kitten Mittons that he orders (as well as any crates that are carried-over in inventory from the previous month). Any unsold crates of Kitten Mittons that remain at the end of each month can be stored in the basement of Paddy's Pub, however Charlie has to pay $5 per month to store each crate and the basement can store at most 46 crates. 15 Table 1: Selling Price ($/Crate) of Kitten Mittons Over Following Twelve Months Month Price Month Price Month Price May September 63 January 38 June 18 October 56 February 47 July 38 November 32 March 51 August 42 December 24 April 41 Charlie has zero crates of Kitten Mittons in inventory currently and wants to determine how to purchase and sell crates of Kitten Mittons over the following twelve months to maximize his profit. Formulate Charlie's problem as a ISE 3210 Spring, 2020 1 dynamic optimization problem by identifying the stages, decision variables, state variables, state-transition functions, constraints, and objective-contribution functions. Problem 1: Charlie Sells Out (30 points) Charlie Kelly has begun producing and marketing a product called Kitten Mittons, which he buys, sells, and stores in inventory in crates, with each crate hold 50 pairs of Kitten Mittons. Table 1 summarizes the prices at which Kitten Mittons will sell over the following twelve months. At the beginning of each month, Charlie can place an order for up to 20 crates of Kitten Mittons, which cost $30 each and are delivered to him immediately. He can sell these crates of Kitten Mittons that he orders (as well as any crates that are carried-over in inventory from the previous month). Any unsold crates of Kitten Mittons that remain at the end of each month can be stored in the basement of Paddy's Pub, however Charlie has to pay $5 per month to store each crate and the basement can store at most 46 crates. 15 Table 1: Selling Price ($/Crate) of Kitten Mittons Over Following Twelve Months Month Price Month Price Month Price May September 63 January 38 June 18 October 56 February 47 July 38 November 32 March 51 August 42 December 24 April 41 Charlie has zero crates of Kitten Mittons in inventory currently and wants to determine how to purchase and sell crates of Kitten Mittons over the following twelve months to maximize his profit. Formulate Charlie's problem as a ISE 3210 Spring, 2020 1 dynamic optimization problem by identifying the stages, decision variables, state variables, state-transition functions, constraints, and objective-contribution functions