ITPEC FE Subject A April 2024 Question 54
A factory manufactures the three products that are shown in the table below. Which of the following is the maximum possible profit in dollars? Here, there is an upper limit to the monthly demand volume for each product. Also, the factory can only use up to 200 hours per month for the manufacturing process and cannot manufacture more than one products in parallel.
Explanation
33,000 dollars — with one time limit, make products in order of profit per minute until demand or time runs out.
Available time: 200 × 60 = 12,000 minutes.
- •X first: 1,000 units use 1,000 × 6 = 6,000 minutes, profit 18,000
- •Y next: the remaining 6,000 minutes make 6,000 ÷ 10 = 600 units (demand allows 900), profit 15,000
- •Z: no time left
Total: 18,000 + 15,000 = 33,000 dollars.
Answer (d)
Why not others:
- •(a) 26,250 — ranks by profit per unit: Z first (500 units, 7,500 minutes, 15,000), then 450 units of Y (11,250)
- •(b) 30,000 — X first, but then Z instead of Y: 400 units of Z in the remaining 6,000 minutes earn only 12,000
- •(c) 31,500 — Y first (900 units, 9,000 minutes, 22,500), then 500 units of X (9,000)
Key rule: When one resource is the bottleneck, rank products by profit per unit of that resource, not by profit per product.
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