$Q1$: Inventory Management

Headline: Streamline Inventory: Compute EOQ and ROP for Component Efficiency

Calculate the Economic Order Quantity $(EOQ)$ and Reorder Point $(ROP)$ for a component with $6,000$ units annual demand, given ordering and holding costs, lead time, and operating days. Show all steps clearly, round $to$ whole numbers, and assume constant demand.

$Q2$: Demand Forecasting

Headline: Predict Demand: June Forecast and May Error via $3-$Month Average

Using $a3-$month moving average, compute the June demand forecast and May$s$ forecast error with historical data $(January-$May$).$ Round $to$ two decimal places, show all calculations step$-by-$step, and ensure accurate forecasting for the company$s$ product planning.

$Q3$: Aggregate Production Planning

Headline: Optimize Costs: $3-$Month Chase Strategy for Production and Inventory

Using a chase strategy, calculate total regular production and inventory holding costs over $3$ months $(January-$March$)$ with forecasted demand. Account for production capacity, costs, and beginning inventory, showing all steps clearly $to$ meet demand without backorders.

$Q4$: Production Line Balancing

Headline: Enhance Efficiency: Cycle Time and Workstations for Line Balancing

Determine the cycle time and minimum workstations needed $to$ produce $40$ units per $8-$hour shift. Use task times, precedence constraints, and formulas, ensuring the line $is$ balanced without exceeding cycle time. Show all calculations clearly.

$Q5$: Safety Stock Calculation

Headline: Secure Supply: Daily Demand and Safety Stock for $95\%$ Service Level

Calculate the average daily demand and safety stock for $a95\%$ service level, given $10,000$ units annual demand, $12-$day lead time, and standard deviation. Round $to$ two deci$5$mal places,