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Arena Simulation. Five identical machines operate independently in a small shop. Each machine is up (i.e.,...

Arena Simulation.

Five identical machines operate independently in a small shop. Each machine is up (i.e., works) for between six and ten hours (uniformly distributes) and then breaks down. There are two repair technicians available, and it takes one technician between one and three hours (uniformly distributed) to fix a machine; only one technician can be assigned to work on a broken machine even if the other technician is idle. If more than two machines are broken down at a given time, they form a (virtual) FIFO repair queue and wait for the first available technician. A technician works on a broken machine until it is fixed, regardless of what else is happening in the system. All uptimes and downtimes are independent of each other. Starting with all machines at the begging of an up time, simulate this for 160 hours and observe the time-average number of machines that are down (in repair or in queue for repair), as well as the utilization of the repair technicians. In Arena, animate the machines when they’re either undergoing repair or in queue for a repair technician and plot the total number of machines down (in repair plus in queue) over time. (Hint: Think of the machine as customers and the repair technicians as servers and note that there are always five machines floating around in the model and they never leave.)

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1 Budgeted manufacturing overhead rate is €4,800,000 ÷ 80,000 = €60 per machine-

hour.

2 Manufacturing overhead underallocated = manufacturing overhead incurred –

manufacturing overhead allocated

= €4,900,000 – €4,500,000*

= €400,000

* €60 × 75,000 actual machine-hours = €4,500,000.

(a)

Account End-of-year

balance (before

proration) (€)

Proration of €400,000

underallocated

manufacturing overhead (€)

Balance (after

proration) (€)

Work in progress 750,000 0 750,000

Finished goods 1,250,000 0 1,250,000

Cost of goods sold 8,000,000

400,000 8,400,000

Total 10,000,000 400,000 10,400,000

(b)

Account End-of-year balance

(before proration) (€)

Proration of €400,000

underallocated

manufacturing overhead (€)

Balance

(after

proration) (€)

Work in progress 750,000 (7.5%) 0.075 × €400,000 = €30,000 780,000

Finished goods 1,250,000 (12.5%) 0.125 × €400,000 = 50,000 1,300,000

Cost of goods

sold

8,000,000

(80.0%) 0.800 × €400,000 = 320,000 8,320,000

Total 10,000,000 (100.0%) €400,000 10,400,000

(c)

Account End-of-year

balance

(before

proration)

(€)

Allocated overhead

component of end-of-

year balance (before

proration) (€)

Proration of €400,000

underallocated

manufacturing overhead

Balance

(after

proration)

(€)

Work in progress 750,000 240,000 (5.33%) 0.0533 × €400,000 = €21,320 771,320

Finished goods 1,250,000 660,000 (14.67%) 0.1467 × €400,000 = 58,680 1,308,680

Cost of goods sold 8,000,000

3,600,000 (80.00%) 0.8000 × €400,000 = 320,000 8,320,000

Total 10,000,000

450,000,000 (100.00%) €400,000 10,400,000

3 Alternative (c) is theoretically preferred to (a) and (b). Alternative (c) yields the same

closing balances in work in progress, finished goods and cost of goods sold that would

have been reported had actual indirect-cost rates been used. The chapter also discusses

an adjusted allocation rate approach that results in the same closing balances as

does alternative (c). This approach operates via a restatement of all the individual

jobs worked on during the year rather than a restatement of closing balances.

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