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Fundamental Information Technology Engineer Examination (FE) | Subject A Operations Research, Inventory, Forecasting, and Accounting Problems 01

1 / 100.0s

Problem 1

Let the production quantities of products X and Y be nonnegative real numbers x and y. Unit profit is 50,000 yen for X and 40,000 yen for Y. The capacities of two facilities impose these constraints: 2x + y <= 10 x + 2y <= 8

Which combination gives the production quantities that maximize profit under linear programming and the resulting profit?

View explanation

The objective is 5x + 4y in units of 10,000 yen. Solving 2x + y = 10 and x + 2y = 8 gives the intersection x = 4 and y = 2, with a profit of 280,000 yen. The other relevant vertices give 250,000 yen at (5,0) and 160,000 yen at (0,4), so the intersection is optimal. Producing only the product with the higher unit profit does not use the two capacities as profitably.

Problem 2

A component has annual demand D = 3,600 units, ordering cost S = 2,000 yen per order, and annual holding cost H = 500 yen per unit. Demand and lead time are constant, with no shortages or quantity discounts. Economic order quantity is Q = sqrt(2DS / H).

What is Q rounded to the nearest whole unit?

View explanation

Q = sqrt(2 × 3,600 × 2,000 / 500) = sqrt(28,800), or approximately 169.7, which rounds to 170 units. EOQ balances annual ordering cost, which falls as order size grows, against annual holding cost, which rises as order size grows.

Problem 3

A product is issued at a constant rate of 40 units per day. Replenishment lead time is five days, and the company maintains 60 units of safety stock. There are no outstanding orders or scheduled receipts, and an order is placed when inventory position reaches the reorder point.

What is the reorder point?

View explanation

Demand during lead time is 40 units per day × 5 days = 200 units. Adding 60 units of safety stock gives a reorder point of 260 units. Safety stock is held in addition to normal lead-time demand to absorb demand increases or replenishment delays.

Problem 4

One of two mutually exclusive investments must be selected. Plan A has a 60% chance of a 12-million-yen profit and a 40% chance of a 3-million-yen loss. Plan B has an 80% chance of a 7-million-yen profit and a 20% chance of a 1-million-yen profit. Expected profit is the only selection criterion.

Which combination correctly gives each plan's expected profit and the resulting choice?

View explanation

A's expected profit is 12 × 0.6 - 3 × 0.4 = 6.0 million yen. B's is 7 × 0.8 + 1 × 0.2 = 5.8 million yen. Under the stated expected-profit-only criterion, A is selected. The 3 million yen in A's unsuccessful outcome is a loss, so it is subtracted rather than added as a positive gain.

Problem 5

A product's demand in the last five months, from oldest to newest, was 100, 120, 140, 160, and 180 units. Simple moving averages are used to forecast next month's demand.

Which statement correctly gives the three-month and five-month forecasts and their response to this upward series?

View explanation

The three-month average is (140 + 160 + 180) / 3 = 160 units. The five-month average is (100 + 120 + 140 + 160 + 180) / 5 = 140 units. Because it excludes the older, lower observations, the shorter average responds more strongly to the recent rise. A shorter period also makes a forecast more responsive to temporary fluctuations.

Problem 6

Demand for the current month was forecast at 200 units, but actual demand was 260 units. Let the smoothing constant alpha be 0.3 and calculate next month's forecast as alpha × current actual + (1 - alpha) × current forecast.

What is next month's demand forecast?

View explanation

The forecast is 0.3 × 260 + 0.7 × 200 = 78 + 140 = 218 units. Alpha is the weight on the new actual value, so a value near zero preserves more of the prior forecast, while a value near one reacts more strongly to the latest actual result.

Problem 7

A machine was observed at 800 randomly selected moments and was operating at 640 of them. Assume this observed proportion represents the full day, whose scheduled duration is 480 minutes.

Which combination gives the utilization and daily operating time estimated by work sampling?

View explanation

Estimated utilization is 640 / 800 = 0.8, or 80%. Estimated operating time is therefore 480 × 0.8 = 384 minutes. Work sampling estimates the overall time composition from the proportions of random instantaneous observations; it does not convert the number of observations directly into minutes.

Problem 8

One hundred defects are classified by cause: A has 40, B has 25, C has 15, D has 10, and E has 10. Causes are addressed in descending order of count, and the smallest set whose cumulative count is at least 80% of all defects must be selected.

Which set of causes should be selected?

View explanation

A and B total 65 defects, or 65%. Adding C brings the cumulative total to 80 defects, or 80%, so A, B, and C are the smallest qualifying set. Including D also exceeds 80%, but it does not meet the requirement to use the fewest categories.

Problem 9

A company has sales of 100 million yen, cost of goods sold of 60 million yen, selling, general, and administrative expenses of 25 million yen, non-operating income of 4 million yen, and non-operating expenses of 2 million yen. Ignore extraordinary items and income taxes.

Which combination correctly gives gross profit, operating profit, and ordinary profit?

View explanation

Gross profit is 100 - 60 = 40 million yen. Operating profit is 40 - 25 = 15 million yen. Ordinary profit is 15 + 4 - 2 = 17 million yen. Non-operating income and expenses enter when ordinary profit is calculated, not when operating profit is calculated.

Problem 10

A company has current assets of 48 million yen and current liabilities of 32 million yen. Net income is 6 million yen, and average total assets are 50 million yen. For this question, current ratio = current assets / current liabilities × 100, and ROA = net income / average total assets × 100.

Which combination correctly gives the current ratio and ROA?

View explanation

The current ratio is 48 / 32 × 100 = 150%, and ROA is 6 / 50 × 100 = 12%. The current ratio uses current liabilities as its denominator to indicate short-term payment capacity. ROA uses average total assets as specified here to indicate the profitability of assets employed.