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Management 2025 Paper II 50 marks Calculate

Paper II — Q3

(a) A company has an annual demand of 1600 units for an item, whose unit cost is ₹70/-. The annual holding cost comprises 18% for…

(a)

A company has an annual demand of 1600 units for an item, whose unit cost is ₹70/-. The annual holding cost comprises 18% for interest charges, 1% for insurance, 1.5% allowances for obsolescence of unit cost and ₹2.50 for building overheads, ₹3.40 for damage loss, and ₹7.0 miscellaneous costs. Placing each order costs the company ₹100/-.

(i)

Calculate Economic Order Quantity (EOQ) and the total costs of stocking the units.

(ii)

If the supplier of the items will only deliver batches of 250 units, how is the total variable cost influenced?

(iii)

If the supplier relaxes their order size requirements, as the company has limited storage space it can stock a maximum of 100 units at any time. What would be the optimal ordering policy and associated costs? 15 marks

3.

(b)

Consider the following aggregate planning problem for four months:

[Table: Regular time | Overtime | Subcontracting; Production capacity/month | 900 units | 300 units | 200 units; Production cost/unit | ₹6/- | ₹8/- | ₹9/-]

The forecasted demand for the next four months is 1300, 1400, 1225 and 1475 units respectively. Shortages are not permitted. The initial inventory is 50 units, and the carrying cost is ₹1.60 per unit per month.

Provide the aggregate plan for this problem. 15 marks

3.

(c)

The warehouse owner of Quick Industries is considering a new computer system for accounting and inventory control. A computer vendor sent the following information about the system installation:

[Table: Activity Identification | Activity description | Immediate Predecessor | Time (Days) (Most optimistic | Most likely | Most pessimistic); A | Selection of Computer Model | - | 5 | 7 | 9; B | Input/output System Design | A | 6 | 8 | 16; C | Monitoring System Design | A | 5 | 9 | 13; D | Computer Hardware Assembly | B | 16 | 21 | 26; E | Development of main Programs | B | 11 | 19 | 27; F | Input/output routines development | C | 9 | 10 | 17; G | Database Creation | E | 5 | 9 | 13; H | Installation of the system | D, F | 2 | 3 | 4; I | Testing and Implementation | G, H | 7 | 8 | 9]

(i)

Draw the network diagram for this information. Identify the Critical Path and expected project completion time.

(ii)

Calculate the probability that the project will be completed in 61 days.

(iii)

When the company wants to be 95% sure that the system will be installed by a certain date, how many days prior to that should it start the work? 20 marks

हिंदी में प्रश्न पढ़ें
(a)

एक कंपनी में किसी वस्तु की वार्षिक मांग 1600 इकाई है जिसकी लागत प्रति इकाई ₹70/- है। वार्षिक होल्डिंग लागत व्याज शुल्क के रूप में 18%, बीमा के लिए 1%, इकाई लागत के अप्रचलन के लिए 1.5% भत्ता, भवन उपरिव्यय ₹2.50, क्षति हानि के लिए ₹3.40 और विविध लागत ₹7.0 है। प्रत्येक आर्डर देने में कंपनी को ₹100/- का खर्च आता है।

(i)

आर्थिक आदेश मात्रा (ई ओ क्यू) की गणना कीजिए और स्टॉकिंग इकाइयों की कुल लागत गणना कीजिए।

(ii)

यदि वस्तुओं का आपूर्तिकर्ता 250 इकाइयों के खेप (बैच) में ही वितरण करता है तो कुल परिवर्तनीय लागत कैसे प्रभावित होगी?

(iii)

चूँकि कंपनी के पास सीमित संग्रह स्थान है, आपूर्तिकर्ता अपने आदेश आकार के आवश्यकताओं में ढील देने को तैयार है। अगर 100 इकाई ही किसी समय भंडार किया जा सकता है तो इष्टतम आदेश (आर्डरिंग) नीति क्या होगी और संबंधित लागत क्या होगी? (15 अंक)

3.

(b)

निम्नलिखित समग्र नियोजन समस्या को चार महीनों के लिए विचार कीजिए:

[टेबल: नियमित समय | अधिक समय तक | उपपट्टू करना; उत्पादन क्षमता/माह | 900 इकाई | 300 इकाई | 200 इकाई; उत्पादन लागत/इकाई | ₹6/- | ₹8/- | ₹9/-]

अगले चार महीनों के लिए मांग पूर्वानुमान क्रमश: 1300, 1400, 1225 और 1475 इकाई है। किसी भी चीज की कमी की अनुमति नहीं है। आरंभिक माल 50 इकाई है और वहन करने की लागत ₹1.60 प्रति इकाई प्रति माह है।

इस समस्या हेतु समग्र योजना उपलब्ध कराइए। (15 अंक)

3.

(c)

Quick Industries के गोदाम मालिक मालसूची नियंत्रण और लेखांकन के लिए एक न्यू कंप्यूटर सिस्टम पर विचार कर रहा है। एक कंप्यूटर विक्रेता ने सिस्टम स्थापित करने के लिए निम्नलिखित जानकारी दी है:

[टेबल: गतिविधि पहचान | गतिविधि विवरण | तत्काल पूर्ववर्ती | समय (दिनों में) (सबसे अधिक आशावादी | सबसे अधिक सम्भावना | सबसे निराशावादी); A | कंप्यूटर मॉडल का चयन | - | 5 | 7 | 9; B | इनपुट/आउटपुट सिस्टम वास्तुकला | A | 6 | 8 | 16; C | सिस्टम वास्तुकला की निगरानी | A | 5 | 9 | 13; D | कंप्यूटर के भौतिक भाग को जोड़ना | B | 16 | 21 | 26; E | मैन प्रोग्राम का विकास | B | 11 | 19 | 27; F | इनपुट/आउटपुट का व्यवस्थित विकास | C | 9 | 10 | 17; G | डेटाबेस बनाना | E | 5 | 9 | 13; H | सिस्टम की स्थापना | D, F | 2 | 3 | 4; I | परीक्षण एवं कार्यान्वयन | G, H | 7 | 8 | 9]

(i)

इस जानकारी से जाल तंत्र (नेटवर्क) आरेख खींचिए। महत्वपूर्ण पथ की पहचान कीजिए और अपेक्षित परियोजना पूर्ण होने का समय बताइए।

(ii)

61 दिनों में इस परियोजना के पूरे होने की संभावना की गणना कीजिए।

(iii)

जब कंपनी 95% निश्चित करना चाहती है कि सिस्टम एक निश्चित तिथि तक स्थापित कर दिया जाय, ज्ञात कीजिए कि उसे कितने दिन पूर्व, कार्य को प्रारंभ करना चाहिए? (20 अंक)

Q3 of the 2025 UPSC Mains Management Paper II, as printed
The question as printed in the 2025 Management paper
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Model answer

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3.(a)(i) Annual holding cost H = 0.18×70 + 0.01×70 + 0.015×70 + 2.50 + 3.40 + 7.00 = ₹27.25 per unit per year. Using EOQ = √(2DS/H): EOQ = √(2×1600×100/27.25) = √(1,280,000/109) ≈ 108.37 units. Total variable stocking cost = D S/Q + H Q/2 = √(2DSH) = √(8,720,000) = 200√218 ≈ ₹2,952.96/year. Purchase cost = 1600×70 = ₹112,000/year. Total stocking cost including purchase ≈ ₹114,952.96/year.

3.(a)(ii) If Q = 250 units: TVC = 1600×100/250 + 27.25×250/2 = 640 + 3,406.25 = ₹4,046.25/year. Increase over EOQ cost = 4,046.25 − 2,952.96 = ₹1,093.29/year.

3.(a)(iii) Since EOQ 108.37 > 100, the storage constraint is binding, so optimal Q* = 100 units. TVC = 1600×100/100 + 27.25×100/2 = 1,600 + 1,362.50 = ₹2,962.50/year. Orders per year = 1600/100 = 16; order interval = 365/16 ≈ 22.81 days. Total including purchase = 112,000 + 2,962.50 = ₹114,962.50/year.

3.(b) Net month-1 demand after initial stock = 1300 − 50 = 1250. Total production needed = 5400 − 50 = 5350 units. Use all regular and overtime: 3600 + 1200 = 4800 units; hence subcontracting = 550 units. Month 4 demand exceeds capacity by 75 units, so carry 75 units from month 3.

  • Month 1: Regular 900, Overtime 300, Subcontract 50; cost = 900×6 + 300×8 + 50×9 = ₹8,250.
  • Month 2: Regular 900, Overtime 300, Subcontract 200; cost = ₹9,600.
  • Month 3: Regular 900, Overtime 300, Subcontract 100; cost = ₹8,700; ending inventory = 1300 − 1225 = 75 units.
  • Month 4: Regular 900, Overtime 300, Subcontract 200; opening inventory 75; cost = ₹9,600.

Total production cost = 8,250 + 9,600 + 8,700 + 9,600 = ₹36,150. Carrying cost = 75×1.60 = ₹120. Total aggregate-plan cost = ₹36,270.

3.(c)(i) Expected times using te = (a + 4m + b)/6: A = 7, B = 9, C = 9, D = 21, E = 19, F = 11, G = 9, H = 3, I = 8 days. Network arrows: A→B,C; B→D,E; C→F; E→G; D,F→H; G,H→I. Paths: A-B-D-H-I = 48 days; A-B-E-G-I = 52 days; A-C-F-H-I = 38 days. Critical path = A→B→E→G→I; expected completion time = 52 days.

Diagram: PERT network

Critical-path variance = 4/9 + 25/9 + 64/9 + 16/9 + 1/9 = 110/9, so σ = √110/3 ≈ 3.496 days. This uses the PERT normal approximation with independent activity times.

3.(c)(ii) z = (61 − 52)/(√110/3) = 27/√110 ≈ 2.574. P(T ≤ 61) = Φ(2.574) ≈ 0.9950. Probability ≈ 99.50%.

3.(c)(iii) For 95% confidence, z = 1.645. Required duration = 52 + 1.645×(√110/3) ≈ 52 + 5.75 = 57.75 days. Start about 58 days before the target installation date.

How this answer will be evaluated

Framework: EOQ Model, Aggregate Planning, PERT

What earns full marks: Precise calculations with correct logic and clear presentation of all constraints.

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Determine EOQ, total stocking cost, and cost impact of batch/limit constraints. 15 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • H = ₹27.25 (percentages on ₹70 plus fixed elements); EOQ ≈ 108.37 units (~14.8 orders/yr)
    • TVC at EOQ = √(2DSH) ≈ ₹2,952.96; purchase 1600×70 = ₹1,12,000; stocking total ≈ ₹1,14,952.96
    • Q = 250: TVC = ₹640 + ₹3,406.25 = ₹4,046.25 → +₹1,093.29 vs EOQ
    • Storage cap 100: Q* = 100 → TVC ₹2,962.50 (~₹9.54 above EOQ); 16 orders; interval ≈22.81 days

    Loses marks

    • Holding cost built from the percentages alone (₹14.35) or the rupee items alone (₹12.90)
    • Applying the percentages to something other than the ₹70 unit cost
    • Comparing the 250-unit and 100-unit policies without computing both ordering and holding cost

    Earns more

    • All six components of holding cost added, percentage ones applied to the ₹70 unit cost
    • Cost comparison stated in rupees, with the EOQ cost as the base

    Extra mark

    • Sensitivity analysis on holding cost components
  2. (b) Develop a 4-month aggregate plan minimizing total production and inventory costs. 15 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Net requirement 5350; month-wise schedule using regular/overtime/subcontract (no shortages)
    • Costs: M1 ₹8,250; M2 ₹9,600; M3 ₹8,700 (ending inventory 75); M4 ₹9,600
    • Total production ₹36,150 + carrying (75×₹1.60 = ₹120) = ₹36,270
    • Satisfies demands 1300/1400/1225/1475; all capacities respected

    Loses marks

    • Shortages in any month
    • Ignoring initial inventory of 50 units

    Earns more

    • Logical allocation of production modes
    • Minimization of inventory holding

    Extra mark

    • Comparison of alternative feasible plans
  3. (c) Analyze project network to find critical path, completion probability, and start date. 20 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • te values (A7, B9, C9, D21, E19, F11, G9, H3, I8) and variances (b−a)²/36
    • Network diagram provided (figure); paths ABDHI=48, ABEGI=52, ACFHI=38
    • Critical path A-B-E-G-I; expected duration 52 days; variance 110/9 → σ ≈ 3.496
    • P(≤61 days): z = 2.574 → ≈0.9950; 95% start: 52 + 1.645σ ≈ 57.75 ≈ 58 days before

    Loses marks

    • Incorrect critical path identification
    • Error in variance calculation

    Earns more

    • Correct network diagram construction
    • Accurate standard deviation calculation

    Extra mark

    • Identification of near-critical paths
What "Calculate" is asking you to do

Apply the standard formula or schedule to data the question has already supplied — a table of readings, cost records, a balance sheet — and produce the number. The method is rarely in doubt; the marks sit in the named intermediate quantities, each of which has to appear as a labelled line.

Structure that answers it

Data as given → formula or standard treatment, named → substitution → each intermediate, labelled → result with units

Where marks are lost

Omitting an intermediate the marking scheme pays for separately, or rounding at an intermediate line so the final figure drifts. In commerce and accountancy, any figure in a statement that no numbered working note supports is treated as unearned.

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