(Solved): Question 1: Process Capacity Analysis A manufacturing plant produces widgets using three machines o ...

Question 1: Process Capacity Analysis A manufacturing plant produces widgets using three machines operating in parallel. Machine A produces 120 ?widgets per hour with a defect rate of \( 5 \% \), ?Machine B produces 150 ?widgets per hour with a defect rate of \( 3 \% \), ?and Machine C produces 100 ?widgets per hour with a defect rate of \( 4 \% \). ?The plant operates for 8 ?hours per day. a) ?Calculate the effective output (good widgets) ?per hour for each machine. b) ?Determine the total effective daily output of the plant. Question 2: Inventory Management A retail store sells a product with an annual demand of 12,000 ?units. The ordering cost is \( \$ 50 \) ?per order, and the holding cost is \( \$ 2 \) ?per unit per year. The store operates 300 ?days per year, and the lead time for restocking is 5 ?days. a) ?Calculate the Economic Order Quantity (EOQ). b) ?Determine the reorder point, assuming a constant daily demand. Question 3: Demand Forecasting A company records the following monthly sales data for a product over the past six months, as shown in the table below: Question 3: Demand Forecasting A company records the following monthly sales data for a product over the past six months, as shown in the table below: Table 1: Monthly Sales Data a) Using a 3-month moving average, forecast the demand for the next month (month 7). b) Using exponential smoothing with a smoothing constant of 0.2 and assuming the forecast for month 1 was 200 units, calculate the forecast for month 7. Question 4: Production Scheduling A factory produces two products, X and Y , on a single machine. The machine requires a setup time of 2 hours when switching from X to Y and 3 hours when switching from Y to X . Product X takes 0.5 hours per unit to produce, and Product Y takes 0.8 hours per unit. The factory needs to produce 100 units of X and 80 units of Y in a week, and the machine is available for 40 hours. a) Calculate the total production time required for both products (excluding setup times). b) Determine the minimum number of setups required and the total time (production setup) to meet the demand. Assume the factory can choose the production sequence. Question 5: Process Flowchart Based on the production process described in Question 4, draw a flowchart to illustrate the sequence of steps for producing Products X and Y. Include the following steps: receiving raw materials, setting up the machine, producing Product X, producing Product Y, inspecting finished products, and packaging. Clearly indicate decision points for switching between products and any looping structures for repeated production. 5