Mechanical Engineering 2023 Paper I 50 marks Solve

Q6

(a) 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) (b) 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 | (i) First Come First Serve (FCFS) (ii) Earliest Due Date (EDD) (iii) Minimum Slack (SLACK) (iv) Shortest Processing Time (SPT) Which sequencing rule among these four rules will be recommended by you? (20 marks) (c) 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

(a) 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) (b) 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 | (i) पहले आओ पहले पाओ (FCFS) (ii) जल्द-से-जल्द नियत तिथि (EDD) (iii) न्यूनतम शैथिल्य (SLACK) (iv) न्यूनतम प्रक्रमण समय (SPT) आपके द्वारा इन चारों में से कौन-से अनुक्रमण नियम की सिफारिश की जाएगी ? (20 अंक) (c) 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)

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How this answer will be evaluated

Approach

Solve all three parts systematically, allocating time proportional to marks: ~40% on part (a) for Taylor's tool life equation and machinability index calculation; ~40% on part (b) for sequencing rules and performance metrics; ~20% on part (c) for break-even analysis with quadratic revenue function. Present each part with clear headings, show all formulas before substitution, and conclude with comparative analysis for part (b) recommendation.

Key points expected

  • Part (a): Apply Taylor's tool life equation VT^n = C; determine constants n and C from given data for materials X and Y; calculate cutting speeds at T=50 min; relative machinability = V_Y/V_X at same tool life
  • Part (b)(i)-(iv): Generate sequences FCFS (A-B-C-D-E), EDD (C-E-A-D-B), SLACK (C-E-A-D-B), SPT (C-A-E-D-B); compute flow time, tardiness, lateness for each job under each rule
  • Part (b): Calculate mean flow time, average tardiness, number of tardy jobs for each rule; construct comparison table with metrics
  • Part (c): Total variable cost = ₹2250/unit; Total cost = 10,00,000 + 2250D; Revenue = 4D²; solve 4D² - 2250D - 10,00,000 = 0 for break-even demand
  • Part (c): Select economically feasible positive root; reject negative demand solution; state final answer in whole units
  • Part (b) recommendation: Justify preferred rule based on objective (e.g., SPT for mean flow time minimization, EDD for due date performance, SLACK for urgency)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies Taylor's equation VT^n=C for part (a) with proper log-log transformation; identifies correct sequencing rules for part (b) with accurate slack calculation (Due Date - Processing Time); sets up quadratic break-even equation for part (c) recognizing revenue varies with demand squaredUses Taylor's equation but with minor exponent errors; sequences mostly correct but one rule confused (e.g., treats SLACK as EDD); linear break-even approach attempted for part (c) missing quadratic natureWrong formula (e.g., uses cutting speed directly without Taylor's equation); fundamental misunderstanding of sequencing rules (e.g., random ordering); treats selling price as constant in part (c)
Numerical accuracy25%12.5Part (a): n, C values correct to 3 decimal places; V_X and V_Y at 50 min accurate; machinability ratio precise. Part (b): All four sequences correct; flow times, tardiness, lateness computed without arithmetic errors. Part (c): Quadratic solution D = [2250 ± √(2250² + 16000000)]/8 correct; selects D ≈ 569 unitsCorrect final answers but minor calculation slips (e.g., one tardiness value wrong in part b); correct quadratic formula but rounding errors; machinability ratio direction reversedSignificant errors in log calculations for Taylor's constants; multiple sequence errors; fails to solve quadratic or uses wrong formula (D = -b ± √... without /2a)
Diagram quality10%5Clear Gantt chart or timeline diagram for at least two sequencing rules in part (b) showing job start/end times; labeled axes with time scale; visual comparison of completion times across rulesBasic table format with completion times but no visual timeline; or diagram present but missing labels/scaleNo diagrams or charts; purely tabular presentation without any visual aid for sequencing comparison
Step-by-step derivation25%12.5Part (a): Shows log(V1) + n·log(T1) = log(V2) + n·log(T2) setup; solves simultaneous equations for n and C explicitly. Part (b): Lists each sequence generation logic step-by-step; shows completion time accumulation. Part (c): Expands TC = FC + VC×D and TR = 4D²; sets TR=TC; applies quadratic formula with discriminant calculationShows key steps but skips some intermediate algebra (e.g., jumps to n value without showing log calculation); sequences stated without showing how obtained; quadratic solved but steps condensedFinal answers only with no derivation; or major steps missing (e.g., n and C stated without calculation from given data points)
Practical interpretation20%10Part (a): Interprets machinability index >1 or <1 meaning for material Y vs X; relates to tool material selection. Part (b): Explicitly recommends rule with justification based on shop floor objective (e.g., SPT for WIP reduction, EDD for customer satisfaction). Part (c): Discusses economic feasibility of two roots and why negative demand rejected; comments on high break-even point implications for pricing strategyStates numerical results but minimal interpretation; generic recommendation without linking to specific metrics; mentions break-even meaning but no strategic insightNo interpretation of machinability significance; no recommendation in part (b) or arbitrary choice without justification; no discussion of why one quadratic root is rejected

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