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3. A store opens from Monday to Friday. The demand of one of its products is iid having distribution 0 2 Pr(D = d) .2 .5 .3 4 The product is sold at $200 per item. Each unsold item by the end of Friday incurs a $10 restocking fee to be sold in the future. If the store runs out of the product during the week, additional demands are lost. If by the end of Friday the store has 0 items, it makes an order of 4 items that will arrive early Monday morning. Each order incurs a $50 fixed cost plus $100 for each ordered item. The store starts with 4 items in stock. (a) Assuming X,, represent the number of items in the store at the end of n-th Friday, give state space S and its transition matrix. (b) | Set up all equations to calculate stationary distribution . You don't need to solve them. (c) | Calculate the expected weekly profit (from the end of this Friday to the end of next Friday) when there is O item at the end of this Friday. You need to consider the cost incurred this week and the revenue earned next week