Two Tender Quotes for a Register Print Order
A Delhi government department must print between 320 and 560 bound registers for an upcoming recruitment cycle; the exact figure will be known only after the vacancy list is finalised. Two quotations, both inclusive of paper and binding, are on the table. Quote A asks a fixed ₹18,500 plus ₹42 for every register beyond the first 200. Quote B asks a fixed ₹9,000 plus ₹58 for each of the first 200 registers and ₹34 for every register beyond 200. Both firms deliver in three weeks and both are registered dealers, so the applicable GST is identical and does not change the ranking. The store officer prefers A because its marginal rate looks lower; the accounts officer prefers B because its fixed charge is smaller. The purchase committee must recommend one firm on 1 April. A supplementary order may be placed later at the same rates, and ₹40,000 (excluding tax) is available from the current quarter's budget.
1. Compute the total payable to each firm at 320 registers and at 560 registers, and state which firm is cheaper at each quantity.
Read the worked answer
At 320 registers:
- A = 18,500 + 42 × (320 − 200) = 18,500 + 5,040 = ₹23,540
- B = 9,000 + 58 × 200 + 34 × 120 = 9,000 + 11,600 + 4,080 = ₹24,680
- A is lower by ₹1,140.
At 560 registers:
- A = 18,500 + 42 × 360 = ₹33,620
- B = 9,000 + 11,600 + 34 × 360 = 9,000 + 11,600 + 12,240 = ₹32,840
- B is lower by ₹780.
The ranking reverses because the two quotations differ in structure, not just in rate. A charges nothing for the first 200 units but levies a steep ₹42 on every extra unit; B charges a high ₹58 on the first 200 but only ₹34 thereafter, and its fixed charge is less than half of A's. Comparing marginal rates alone (A ₹42 vs B ₹34) is therefore misleading at low volume, and comparing fixed charges alone is misleading at high volume. Only the total at the actual quantity is a valid basis.
2. Find the quantity at which the two quotations cost the same, and use it to advise the committee if the final figure is expected to be about 480, with a possible swing up to 640.
Read the worked answer
Set the totals equal, with Q > 200: 18,500 + 42(Q − 200) = 9,000 + 11,600 + 34(Q − 200) 10,100 + 42Q = 13,800 + 34Q 8Q = 3,700 → Q = 462.5
Check: at Q = 462, A = ₹29,504 and B = ₹29,508 (A ahead by ₹4); at Q = 463, A = ₹29,546 and B = ₹29,542 (B ahead by ₹4). The crossover is therefore between 462 and 463 registers.
At the expected 480: A = 18,500 + 42 × 280 = ₹30,260; B = 20,600 + 34 × 280 = ₹30,120 → B saves ₹140. At 640: A = 18,500 + 42 × 440 = ₹36,980; B = 20,600 + 34 × 440 = ₹35,560 → B saves ₹1,420.
Recommendation: award to B. Every quantity at or above the expected 480 lies on B's side of the crossover, and B's exposure is smaller if the order shrinks, because its fixed charge is ₹9,000 against ₹18,500. A would be justified only if the department could commit in writing to a quantity at or below 462.
3. Firm A offers to revise only its post-200 rate. What rate would make A exactly equal to B at 640 registers, and should the committee pursue that concession?
Read the worked answer
A's total at 640 is 18,500 + 440r, where r is the revised post-200 rate. Setting this equal to B's ₹35,560: 440r = 35,560 − 18,500 = 17,060 → r = ₹38.77 per register (about ₹38.80, against the quoted ₹42, a cut of roughly 7.7%).
At r = ₹38.77, A also becomes cheaper at every other quantity in the working range: at 480, A = 18,500 + 280 × 38.77 = ₹29,356 against B's ₹30,120; at 320, A = 18,500 + 120 × 38.77 = ₹23,152 against B's ₹24,680. A concession at this level therefore removes the crossover problem entirely and makes the award insensitive to the final quantity.
Should the committee chase it? It is legitimate to invite a written revised offer before the award is finalised, and a 7.7% reduction on the variable component is not implausible for a firm with unused capacity. But the committee must not treat a post-tender revision as a substitute for evaluating the sealed offers, must obtain the revision in writing with a validity period, and must satisfy itself that the lower rate does not imply thinner paper or weaker binding. If A's original offer stands, the award goes to B.