Write a linear program in abstract form that could be used to solve the following problem: Problem Description: Multi$-$Period Inventory Management for Hospital Medical Supplies Background: You are responsible for managing the inventory of n critical medical supplies at a hospital over a $12$ month planning horizon. Given the hospital$$s limited storage capacity and fluctuating monthly demand for medical supplies, maintaining an optimal balance of stock is essential. The purchasing cost of each supply, as well as holding costs for stored inventory, vary each month. Your goal is to minimize the total inventory$-$related costs, which include the cost of purchasing supplies and holding costs, while ensuring that demand is met each month to avoid shortages. Assume uniform supply consumption throughout the month, and a lead time on orders of $(1)/(2)$ a month. Each month, you begin with a certain stock level and can decide how many additional supplies to purchase to meet anticipated demand and prepare for future periods. The hospital$$s storage capacity imposes limits on the maximum quantity of all supplies that can be held at any given time. For the sake of this model assume all n supplies are of the same size and shape. Monthly Sequence of Events: $1.$ Observation $($a$)$: Observe the current stock level of medical supplies at the beginning of the month. $2.$ Demand Fulfillment $($b$)$: Allocate inventory to meet the monthly demand, constrained by available stock. $3.$ Purchasing $($c$)$: Decide on the quantity of supplies to purchase at the current month$$s price, ensuring that total stock does not exceed storage capacity. $4.$ Holding $($d$)$: Calculate holding costs based on the remaining inventory at the end of each month. Objective: Formulate a linear programming model to determine the optimal monthly purchasing and inventory holding strategy. The objective is to minimize total costs over the $12-$month period, considering: $$ Monthly purchasing costs for new supplies. $$ Monthly holding costs for inventory on hand. $$ Demand constraints to ensure all supply needs are met each month. $$ Storage constraints to prevent stock from exceeding storage capacity at any time.