A local stationary store is well-known for its excellent selection of products and caters to customers...

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A local stationary store is well-known for its excellent selection of products and caters to customers who like to purchase in person rather than online. It is one of the only stationary stores in the area to stock left-handed scissors. But the demand for left-handed scissors is quite small. The purchasing manager has observed that during a typical week, the demand for left- handed scissors is zero with probability 0.3, 1 with probability 0.5 and 2 with probability 0.2. A pair of left-handed scissors costs $3.00 and sells for $8.00. Because there are so few sources, customers will return if the product is out of stock. However, the store has a policy of giving customers a certificate for a $2.00 discount if the store is out of stock and the customer returns to purchase the product later. The store uses an inventory holding cost rate of 100% (2% per week) for products such as scissors. The stationary store's main supplier is willing to supply left-handed scissors overnight, along with the stationary store's regular order, but charges a $5.00 handling fee for orders of these scissors that are not a multiple of 10 (because the manufacturer sells scissors in boxes of 10 to large customers). The manager doesn't think it is sensible to order an entire box at the same time because the average demand for left-handed scissors is less than one per week. (a) What is the Markov transition matrix if the store uses a periodic review policy with s = S=4? A local stationary store is well-known for its excellent selection of products and caters to customers who like to purchase in person rather than online. It is one of the only stationary stores in the area to stock left-handed scissors. But the demand for left-handed scissors is quite small. The purchasing manager has observed that during a typical week, the demand for left- handed scissors is zero with probability 0.3, 1 with probability 0.5 and 2 with probability 0.2. A pair of left-handed scissors costs $3.00 and sells for $8.00. Because there are so few sources, customers will return if the product is out of stock. However, the store has a policy of giving customers a certificate for a $2.00 discount if the store is out of stock and the customer returns to purchase the product later. The store uses an inventory holding cost rate of 100% (2% per week) for products such as scissors. The stationary store's main supplier is willing to supply left-handed scissors overnight, along with the stationary store's regular order, but charges a $5.00 handling fee for orders of these scissors that are not a multiple of 10 (because the manufacturer sells scissors in boxes of 10 to large customers). The manager doesn't think it is sensible to order an entire box at the same time because the average demand for left-handed scissors is less than one per week. (a) What is the Markov transition matrix if the store uses a periodic review policy with s = S=4?

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