GATE ME 2017 Set 2 — Question 48
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumTransportation & AssignmentOperations ResearchIndustrial Engineering
Industrial Engineering → Operations Research → Transportation & Assignment
Last updated
Question
A product made in two factories, P and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:
Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as (in Rupees) and the optimized (minimum) total transportation cost is (in Rupees), then , in Rupees, is
| Factory | Destination R | Destination S |
|---|---|---|
| P | 10 | 7 |
| Q | 3 | 4 |
- A.0
- B.15
- C.35
- D.105
Answer checking is unavailable for this question. You can review the published solution without a score.
Correct answer
(MARK TO ALL)
Solution
Step 1: Calculate the total transportation cost () using the North-West Corner Method (NWCM).
Using the Least Cost Method or Vogel's Approximation Method:
Optimality check using MODI method: . Opportunity cost . Thus, is optimal.Step 3: Calculate .
Rupees.Since 28 is not among the given options, this question was marked as 'Mark to all' in the official GATE 2017 answer key.
- Allocate to cell (P, R): . Remaining Demand for R = 1.
- Allocate to cell (Q, R): . Remaining Supply for Q = 8.
- Allocate to cell (Q, S): .
Using the Least Cost Method or Vogel's Approximation Method:
- Allocate to cell (Q, R) [lowest cost 3]: . Remaining Supply for Q = 1.
- Allocate to cell (Q, S) [next lowest cost 4]: . Remaining Demand for S = 7.
- Allocate to cell (P, S) [remaining cell]: .
Optimality check using MODI method: . Opportunity cost . Thus, is optimal.Step 3: Calculate .
Rupees.Since 28 is not among the given options, this question was marked as 'Mark to all' in the official GATE 2017 answer key.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Operations Research
2026 Set 1 Q46An objective function of primal variables ( and ) is described below: Minimize…2026 Set 1 Q47Four jobs are on order in a factory. As on day 20 of the production calendar, the corresponding due…2026 Set 1 Q60The actual demand for castings in a factory is units and units for the months of…2026 Set 1 Q61The inventory holding cost of an item is ₹ 0.50 per unit per month and the ordering cost per order…2026 Set 1 Q65The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e.,…