colapop requires, an average, 2,700 tons of aluminum each week, with a standard deviation of 700 tons. The lead time to receive its orders is 8 weeks. The holding cost for one ton of aluminum for one week is $9. It operates with a 0.99 in-stock probabilityon average how many tons does it have on hand?if its average inventory was 9000 tons, what would be its average holding cost per week?Suppose its on-hand is 5375 tons, on average, what in stock probability does it offer to customers? **Table 11.5: In-Stock Probabilities and Matching Safety Factors, z**This table provides data on the relationship between in-stock probabilities and their corresponding safety factors. It helps in determining how much safety stock is needed to achieve a desired service level in inventory management.- **Left Column:** - **In-Stock Probability and Safety Factor, z:** - In-Stock Probability: 0.9000, Safety Factor, z: 1.28 - In-Stock Probability: 0.9800, Safety Factor, z: 2.05 - In-Stock Probability: 0.9900, Safety Factor, z: 2.33 - In-Stock Probability: 0.9950, Safety Factor, z: 2.58 - In-Stock Probability: 0.9999, Safety Factor, z: 3.72- **Right Column:** - **Safety Factor and In-Stock Probability:** - Safety Factor, z: 1.25, In-Stock Probability: 0.8944 - Safety Factor, z: 2.00, In-Stock Probability: 0.9773 - Safety Factor, z: 2.25, In-Stock Probability: 0.9878 - Safety Factor, z: 2.50, In-Stock Probability: 0.9938 - Safety Factor, z: 3.00, In-Stock Probability: 0.9987This data is pivotal for calculating the level of inventory required to meet specified service levels in supply chain management.

This question is related to the topic-Inventory Management and this topic falls under the operations management syllabus. Here, the question has been asked to determine the on hand or safety stock inventory, average holding costs per week and in-stock probability, all these calculations are shown in the next step. 1) Safety stock or on-hand inventory could be determined as a Z score value for the in-stock probability of 0.99*Standard deviation of weekly demand*Square root of lead time Safety stock or on-hand inventory=2.33*700*Square root of 8 Safety stock or on-hand inventory=2.33*700*2.828 Safety stock or on-hand inventory=4612.468 2) Average holding costs per week=weekly average Inventory*holding cost for one ton of aluminium for one week Average holding costs per week=9000*9 Average holding costs per week=81000 3) Safety stock or on-hand inventory=Z score value for the in-stock probability of X*700*Square root of 8 Or, Z score value for the in-stock probability of X=5375/(700*2.828) Or, Z score value for the in-stock probability of X=2.7152 From the Z table, we could see the below value, The in-stock probability=0.9808 or 98.08% (Approx.) Note: This is approx. value, actual value could be slightly differered.