ITPEC IP October 2025 Question 68
The entire inventory of Warehouse A and Warehouse B is to be sent to Store C and Store D. The number of items in the inventory of Warehouse A and Warehouse B is 35 and 15 respectively, and the required number of items for Store C and Store D is 20 and 30 respectively. The shipment cost for each item from warehouse to store is as shown in the table. Under these conditions, what is the minimum total shipment cost in dollars?
Unit: dollars/item
Explanation
11,000 dollars — send Warehouse B's 15 items to Store C, where they save the most, and fill the rest from A.
Supply (35 + 15) equals demand (20 + 30), so every item moves. B is cheaper than A for both stores, but B has only 15 items. Its saving over A is 400 − 200 = 200 per item at C and 200 − 100 = 100 per item at D, so B's items go to C.
- •B → C: 15 × 200 = 3,000
- •A → C: the remaining 5 items, 5 × 400 = 2,000
- •A → D: all 30 items, 30 × 200 = 6,000
- •Total: 3,000 + 2,000 + 6,000 = 11,000
In general, with x items from B to C the cost is 12,500 − 100 × x, smallest at x = 15.
Answer (c)
Why not others:
- •(a) 8,500 — ships each warehouse's stock by its cheapest route, 35 × 200 + 15 × 100, sending 35 items to D, which needs only 30
- •(b) 10,000 — supplies all 20 items for C from B at 200 dollars, but B holds only 15
- •(d) 12,500 — sends B's 15 items to D instead of C, using B's smaller saving
Key rule: When cheap capacity is limited, give it to the destination where it saves the most over the alternative, not simply to its cheapest route.
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