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 $\backslash (5\backslash \%\backslash ),$Machine B produces $150$widgets per hour with a defect rate of $\backslash (3\backslash \%\backslash ),$and Machine C produces $100$widgets per hour with a defect rate of $\backslash (4\backslash \%\backslash ).$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 $\backslash (\backslash$$ $50\backslash )$per order, and the holding cost is $\backslash (\backslash$$ $2\backslash )$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 $0\mathrm{.}2$ 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 $0\mathrm{.}5$ hours per unit to produce, and Product Y takes $0\mathrm{.}8$ 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. $5$