IPA FE Subject A sample Question 57
A question IPA Japan published in 基本情報技術者試験 科目A サンプル問題 問57, translated into English. ITPEC is based on the same exams.
Two (2) types of raw materials A and B are required to manufacture products X and Y. The quantity of each raw material required to manufacture one (1) unit of a product and the procurable quantity are as shown in the table. When the sales profit per unit is 100 yen for product X and 150 yen for product Y, what is the maximum profit in yen?
Explanation
7,000 yen — the optimum is the plan that uses up both raw materials.
Let x and y be the units of X and Y. Maximise P = 100x + 150y subject to:
- •Material A: 2x + y ≤ 100
- •Material B: x + 2y ≤ 80
- •x ≥ 0, y ≥ 0
The maximum of a linear program lies at a corner of the feasible region:
The corner (40, 20) solves 2x + y = 100 and x + 2y = 80: doubling the second gives 2x + 4y = 160, subtracting the first leaves 3y = 60, so y = 20 and x = 40. Then P = 100 × 40 + 150 × 20 = 7,000.
Answer (c)
Why not others:
- •(a) 5,000 — makes only X, 50 units limited by material A, leaving part of material B unused
- •(b) 6,000 — makes only Y, 40 units limited by material B, leaving part of material A unused
- •(d) 8,000 — no feasible plan reaches it; for example, 80 units of X would need 160 units of material A against 100 available
Key rule: In a two-variable linear program, evaluate the objective at every corner of the feasible region; the best is usually where the binding constraints intersect, not where one resource is used alone.
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This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.