Using case study attached, help solve below:

$1.$ Based on the information provided for the policy documents and assuming that the company operates $360$ days a year, determine the optimal ordering policy, including the order quantity and reorder point, for this inventory item. Calculate the total annual inventory$-$related cost at optimality and explain how following the optimal strategy could improve various performance measures compared to the company$$s current inventory management practices.

$2.$ For the printer cartridges, determine the optimal ordering policy to minimize the total annual cost, considering the variability in demand and lead time. Identify the customer service measures under this policy and discuss what they indicate about meeting customer demand and satisfaction.

$3.$ Calculate the safety stock levels required to maintain different cycle service levels $($e$.$g$.,95\%,96\%,97\%,98\%,$ and $99\%)$ for the printer cartridges, considering the variability in demand and lead time. For each service level, determine the reorder point and the total inventory$-$related cost. Discuss how these different service levels could impact the company$$s ability to improve customer satisfaction without incurring excessive costs.

$4.$ Determine the optimal order quantity for the marketing materials needed for the upcoming campaign. Consider the trade$-$offs between the costs of overstocking and understocking.

$5.$ Given the current capacity constraints of the storage facility and the impending increase in inventory due to the upcoming marketing campaign, discuss whether the company may need to lease additional storage space after optimizing its current inventory practices. What factors should be considered in making this decision? If leasing additional storage space is not feasible, what would be your recommendation to reduce the overall inventory levels so that the company can have enough storage space for the upcoming campaign?

Capstone Project $-$ Phase V

As the Chief Operations Officer $($COO$)$ of Trust Guard Insurance, your ongoing mission has been

to refine and optimize various operational aspects of the company. With several improvements

already implemented in the processing of policies and customer service, your focus now shifts to

a more behind$-$the$-$scenes but equally critical component: Inventory Management. This area,

though less visible to the customer, plays a pivotal role in ensuring that every other department

functions smoothly and without interruption.

The New Policy Issuance Department, for instance, relies heavily on a steady supply of policy

documents, printer cartridges, and other office supplies. If any of these materials were to run out

unexpectedly, the repercussions would ripple through the company, affecting everything from

policy issuance to customer satisfaction. The company's marketing team, too, depends on timely

access to promotional materials and other marketing collateral to effectively execute campaigns

that attract and retain customers.

At the heart of Trust Guard Insurance's operations is a centralized inventory system that manages

all these supplies. However, recent assessments have revealed significant inefficiencies in how

inventory is managed. The inventory management practices currently in place are inconsistent and

lack a coherent strategy tailored to the specific needs of each type of item. This has led to situations

where the company either holds excess inventory, tying up valuable capital and incurring

unnecessary storage costs, or experiences stockouts, disrupting operations and negatively

impacting customer satisfaction. These inconsistent practices have led to tangible issues, such as

increased costs and inefficiencies, highlighting the need for a more strategic approach to inventory

management.

For example, policy documents, which are in constant demand, have been ordered in large

quantities without a clear understanding of how much should be kept on hand to minimize costs.

The annual demand for these documents is estimated to be $10,000$ units. The ordering cost from

the supplier, who specializes in high$-$quality, customizable printed materials for insurance

companies, is $$50$ per order, with a lead time of about $7$ days. Each policy document costs $$8,$ and

the inventory carrying rate is $25\%$ of the item's cost per year. However, the company has been

struggling with determining the optimal order quantity and often either orders too much, leading

to high holding costs, or too little, resulting in frequent reorders and stockouts.

The demand for printer cartridges, on the other hand, is highly variable, with frequent spikes during

periods of high policy issuance or large$-$scale marketing campaigns that require significant

printing. The historical data shows that demand for printer cartridges follows a normal distribution,

with an average daily demand of $20$ units and a daily standard deviation of $5$ units. The company

has not established a clear approach to managing thi

for printer cartridges has a lead time