Paper I — Q6
(a) Following data were observed while machining two different work materials X and Y using a centre lathe machine: If work…
Following data were observed while machining two different work materials X and Y using a centre lathe machine:
If work material X is standard material, then determine the relative machinability considering the tool life of 50 minutes as criterion. 20 marks
The work processing time and due date of five jobs are given in the following table. These five jobs are to be sequenced as per:
| Jobs | Processing Time (days) | Due Date (days) |
|---|---|---|
| A | 5 | 10 |
| B | 10 | 15 |
| C | 2 | 5 |
| D | 8 | 12 |
| E | 6 | 8 |
First Come First Serve (FCFS)
Earliest Due Date (EDD)
Minimum Slack (SLACK)
Shortest Processing Time (SPT)
Which sequencing rule among these four rules will be recommended by you? 20 marks
A company is producing pumps. The cost of the structure of a pump is as under:
Material cost: ₹ 1000/unit Labour cost: ₹ 500/unit Variable cost overheads: 50% of labour and material cost
If the fixed cost for the production of pumps amounts to ₹ 10,00,000 and selling price (S) varies as S = 4D², where D is demand in units, how many items will the company have to sell to reach break-even point? 10 marks
हिंदी में प्रश्न पढ़ें
केन्द्र खराद मशीन पर दो विभिन्न कार्य पदार्थ X और Y के मशीनिंग के दौरान निम्नांकित आँकड़े मिले :
यदि कार्य पदार्थ X मानक पदार्थ है, तो औजार की उम्र को 50 मिनट आधार मानते हुए सापेक्षिक मशीनिंग-सुकरता ज्ञात कीजिए । (20 अंक)
पाँच कृत्यों का प्रक्रमण समय तथा नियत तिथि निम्नांकित तालिका में दिए हुए हैं । इन पाँचों कृत्यों को निम्नांकित तरीके से क्रमबद्ध (अनुक्रमण) किया जाना है :
| कृत्य | प्रक्रमण समय (दिन) | नियत तिथि (दिन) |
|---|---|---|
| A | 5 | 10 |
| B | 10 | 15 |
| C | 2 | 5 |
| D | 8 | 12 |
| E | 6 | 8 |
पहले आओ पहले पाओ (FCFS)
जल्द-से-जल्द नियत तिथि (EDD)
न्यूनतम शैथिल्य (SLACK)
न्यूनतम प्रक्रमण समय (SPT)
आपके द्वारा इन चारों में से कौन-से अनुक्रमण नियम की सिफारिश की जाएगी ? (20 अंक)
एक कंपनी पंप बनाती है । पंप की संरचना की लागत निम्न प्रकार है :
सामग्री लागत : ₹ 1000/इकाई श्रमिक लागत : ₹ 500/इकाई परिवर्तनशील ऊपरि लागत : श्रमिक और सामग्री लागत का 50%
यदि पंप बनाने की स्थिर लागत ₹ 10,00,000 है तथा विक्रय मूल्य (S), S = 4D², (जहाँ D माँग इकाई के रूप में) के अनुसरूप बदल रहा हो, तो ब्रेक-ईवन (लाभ-अलाभ) बिंदु तक पहुँचने के लिए कंपनी को कितनी इकाइयाँ बेचनी होंगी ? (10 अंक)
The figure this question refers to, in words
The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.
(a) Table with columns: Work Material, Cutting Tool Life (min.), Cutting Speed (m/min.). Rows: X, 20, 125 X, 15, 150 Y, 45, 250 Y, 25, 300
(b) Table with columns: Jobs, Processing Time (days), Due Date (days). Rows: A, 5, 10; B, 10, 15; C, 2, 5; D, 8, 12; E, 6, 8.
Model answer
Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.
(a) Relative machinability of Y with respect to X
Use Taylor's tool-life equation VTⁿ = C for the same tool, feed, depth of cut and coolant.
For X: 125 × 20ⁿ = 150 × 15ⁿ, so (20/15)ⁿ = 150/125 = 1.2 and n_X = ln 1.2/ln(4/3) = 0.6338. C_X = 125 × 20^0.6338 = 834.5 m/min (the second point gives the same value). Speed for T = 50 min: V_X = 125(20/50)^0.6338 = 69.9 m/min.
For Y: 250 × 45ⁿ = 300 × 25ⁿ, so (45/25)ⁿ = 1.2 and n_Y = ln 1.2/ln 1.8 = 0.3102. C_Y = 250 × 45^0.3102 = 814.2 m/min. Speed for T = 50 min: V_Y = 250(45/50)^0.3102 = 242.0 m/min.
Relative machinability index (standard material X = 100) at a 50 min tool life: M_Y = (V_Y/V_X) × 100 = (242.0/69.9) × 100 ≈ 346.
Y is therefore about 3.46 times as machinable as X at 50 min tool life. The 50 min speeds are extrapolations from the tested range.
(b) Job sequencing by FCFS, EDD, SLACK and SPT
All five jobs are available at time 0, and total processing time is 31 days. Completion time C is the cumulative processing time, flow time equals C, and tardiness = max(0, C − due date).
(i) FCFS, order A-B-C-D-E: C = 5, 15, 17, 25, 31. Average flow time = 93/5 = 18.6 days. Tardiness = 0, 0, 12, 13, 23, total 48 days (average 9.6), maximum 23, three late jobs.
(ii) EDD, order C-E-A-D-B: C = 2, 8, 13, 21, 31. Average flow time = 75/5 = 15.0 days. Tardiness = 0, 0, 3, 9, 16, total 28 days (average 5.6), maximum 16, three late jobs.
(iii) SLACK (slack = due date − processing time: A 5, B 5, C 3, D 4, E 2), order E-C-D-A-B with the A/B tie broken in favour of A: C = 6, 8, 16, 21, 31. Average flow time = 82/5 = 16.4 days. Tardiness: E 0, C 3, D 4, A 11, B 16; total 34 days (average 6.8), maximum 16, four late jobs.
(iv) SPT, order C-A-E-D-B: C = 2, 7, 13, 21, 31. Average flow time = 74/5 = 14.8 days. Tardiness = 0, 0, 5, 9, 16, total 30 days (average 6.0), maximum 16, three late jobs.
SPT gives the best average flow time (14.8 days), while EDD gives the least total tardiness (28 days, average 5.6) and ties for the lowest maximum tardiness. Because due dates are given, due-date performance matters most. EDD is recommended; SPT would be preferred only if minimum flow time were the sole objective.
(c) Break-even quantity of pumps
Variable overhead = 50% × (1000 + 500) = ₹750/unit. Variable cost per unit v = 1000 + 500 + 750 = ₹2250. Fixed cost F = ₹10,00,000.
The selling price per unit is S = 4D², so total revenue = D × S = 4D³. Break-even: 4D³ = 10,00,000 + 2250D, i.e. 4D³ − 2250D − 10,00,000 = 0. Trying values: at D = 65, 4D³ − 2250D − 10⁶ = 1,098,500 − 146,250 − 1,000,000 = −47,750 (cost exceeds revenue), and at D = 66, 1,149,984 − 148,500 − 1,000,000 = +1,484 (revenue exceeds cost). The root is D ≈ 65.97.
The company must sell 66 pumps to break even. If S were instead read as total sales revenue, 4D² = 10,00,000 + 2250D would give D ≈ 854.9, that is 855 units.
How this answer will be evaluated
What earns full marks: All parts solved with correct formulas, clear steps, and accurate final answers.
Evaluation rubric
Each sub-part is marked on its own, against the marks and word limit printed on the paper.
- (a) Determine the relative machinability of Y with X as standard at 50 min tool life. 20 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Taylor equation VT^n = C
- n_X 0.6338 and n_Y 0.3102
- V50 for X 69.9 and Y 242.0 m/min
- Index of Y about 346
Loses marks
- Comparing speeds at different tool lives.
Earns more
- Marks for Taylor constants, speeds at 50 min and the index.
Extra mark
- Noting extrapolation beyond tested range.
- (b) Sequence five jobs by FCFS, EDD, SLACK and SPT and recommend a rule. 20 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Completion and flow times for each rule
- Tardiness: FCFS 48, EDD 28, SLACK 34, SPT 30
- Average flow time: SPT lowest 14.8 days
- EDD recommended on tardiness
Loses marks
- Not computing tardiness.
Earns more
- Marks for four sequences, performance measures and the recommendation.
Extra mark
- Noting SPT preferred only for flow time.
- (c) Find the break-even quantity of pumps with price S = 4D^2. 10 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Variable cost 2250 per unit
- Revenue D x S = 4D^3
- 4D^3 = 10,00,000 + 2250D
- D about 66
Loses marks
- Using only material and labour as variable cost.
Earns more
- Marks for variable cost, equation and the quantity.
Extra mark
- Mentioning the total-sales reading giving 855.
What "Solve" is asking you to do
Choose the method, then carry it through to a final answer. Identifying what kind of problem this is and why that method applies is the first thing marked; a correct figure arrived at invisibly earns almost nothing.
Structure that answers it
Given data and what is required → method chosen, with the reason it applies → set-up (equation, circuit, free body, trial balance) → working, step by step → answer with units and any condition of validity
Where marks are lost
Doing the middle steps mentally and writing only the result. In mathematics papers, a further loss comes from giving a decimal where the exact value in surds or fractions was wanted, or from skipping the justification a part explicitly asks for.
Practice this exact question
Write your answer and it is marked point by point against the model answer above — what you covered, what you missed, what you got wrong.
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