Operations, Social Initiatives and Process Optimization Practice Questions for XAT: 99+ Solved Questions with Step-by-Step Solutions

    Solve 99+ Operations, Social Initiatives and Process Optimization practice questions for XAT with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Operations and Social Initiatives

    Chapter Roadmap

    1. NGO Operations and Community Kitchens
    Macro-level setup, resource allocation, supply chain, and managing social constraints.
    2. Kitchen Process Optimization and Scheduling
    Micro-level task sequencing, simultaneous activities, bottleneck identification, and time management.

    The Core Intuition: Operations for Social Impact

    The Core Intuition

    A community kitchen is an operations system where the objective function shifts from profit to social impact.

    Input
    Raw ingredients, volunteer labor, donated funds, kitchen space.
    Process
    Procurement, storage, preparation, cooking, packaging, distribution.
    Output
    Meals served, nutritional value delivered, hunger alleviated.
    The Fundamental Challenge
    Apply rigorous operational logic (capacity, bottlenecks) to a scenario where constraints are social, unpredictable, or reliant on human goodwill.

    Operations, Social Initiatives and Process Optimization: Solved Questions with Step-by-Step Explanations (5 Problems)

    Question 1 · Decision Making (DM) MCQ

    In a kitchen scheduling network with multiple paths from start to finish, the critical path is best defined as:

    1. A.

      The path with the shortest total duration

    2. B.

      The path that uses the fewest resources

    3. C.

      The longest sequence of dependent tasks, which determines the minimum completion time

    4. D.

      The path with the most parallel activities

    Correct Answer:

    C

    Step-by-Step Solution

    Key idea: this is a definition-recall question about the critical path, recognizable because it directly asks for the definition of 'critical path' in a scheduling network.

    Step 1: Recall that in a network of tasks, there are multiple paths from start to finish.

    Step 2: The critical path is the longest path (sequence of dependent tasks) through the network.

    Step 3: It determines the minimum possible completion time because all other (shorter) paths can finish within this duration.

    Step 4: It is not about shortest duration (A), fewest resources (B), or most parallel activities (D).

    Answer: The longest sequence of dependent tasks, which determines the minimum completion time.

    Question 2 · Decision Making (DM) MCQ

    An NGO kitchen has 1 prep station and 1 stove. They receive a donation of exactly 14 kg of potatoes, which must be fully used to make Aloo Curry (AC) or Aloo Tikki (AT).

    • AC requires 2 kg potatoes, 20 mins prep, 30 mins cook.
    • AT requires 1 kg potatoes, 30 mins prep, 10 mins cook.

    The kitchen must make at least as many AC as AT.

    Preparation for a dish must be completely finished before its cooking can begin. There is no time lost in transferring a dish. The stove can only cook one dish at a time, but the prep station can prep the next dish while the stove is cooking.

    What is the maximum number of meals they can finish cooking within 220 minutes?

    1. A.

      6

    2. B.

      7

    3. C.

      8

    4. D.

      9

    Correct Answer:

    D

    Step-by-Step Solution

    Key idea: This is a bounding and scheduling synthesis question. We must maximize the number of meals subject to a strict ingredient constraint, a ratio constraint, and a makespan constraint where prep and cook overlap.

    Step 1: Define variables and constraints.

    Let be AC, be AT.

    Potatoes: .

    Ratio: .

    Meals = . Since , Meals = . To maximize meals, we must minimize .

    From .

    So the theoretical minimum for is 5, giving and Meals = 9.

    Step 2: Check if fits in 220 minutes.

    Total prep time = mins.

    Total cook time = mins.

    Since Prep > Cook, the prep station is the bottleneck. The stove will be idle at the end.

    To minimize total time, the stove must start as early as possible. We should prep the item with the shortest cook time first? No, we want the stove to start immediately. The first item takes 30 mins to prep (AT). So the stove starts at 30 mins.

    The stove works continuously for 190 mins. Total time = mins.

    This fits exactly within the 220-minute limit!

    Step 3: Verify other combinations just in case.

    If : Meals = 8. Prep = 180, Cook = 200. Cook is bottleneck. Time = Cook + first prep = . Also fits, but gives fewer meals.

    Since we want the MAXIMUM meals, 9 is the answer.

    Answer: 9

    Question 3 · Decision Making (DM) MCQ

    An NGO runs four community kitchen projects (P, Q, R, S), each producing a different meal. The manager needs to identify the binding constraint and the maximum weekly output for each project.

    Project P (Soup): Has 100 kg of vegetables, but 10% is wasted before use. Requires 2 kg of usable veg per 10 liters of soup. Takes 1 hour to cook 10 liters. Has 40 hours/week, but 2 hours are lost to setup.

    Project Q (Bread): Has 60 kg of flour. Requires 1 kg of flour per 5 loaves. Takes 0.5 hours to bake 5 loaves. Has 30 hours/week, but the oven requires 1 hour of preheating before any baking.

    Project R (Rice): Has 50 kg of rice. Requires 1 kg of rice per 20 meals. Takes 15 minutes to cook 20 meals. Has 20 hours/week, but the rice must soak for 1 hour before cooking can begin.

    Project S (Dal): Has 45 kg of lentils. Requires 1 kg of lentils per 15 meals. Takes 20 minutes to cook 15 meals. Has 25 hours/week with no setup or soak times.

    Match each project to its Binding Constraint and Maximum Weekly Output:

    List II:

    1. Ingredient, 1000 meals
    2. Time, 380 liters
    3. Ingredient, 675 meals
    4. Time, 290 loaves
    1. A.

      P-2, Q-4, R-1, S-3

    2. B.

      P-2, Q-1, R-4, S-3

    3. C.

      P-4, Q-2, R-1, S-3

    4. D.

      P-2, Q-4, R-3, S-1

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: This is a capacity planning and bottleneck identification question with hidden unit conversions and setup times. We must calculate the maximum output from both ingredients and time for each project, then find the minimum (the binding constraint).

    Step 1: Analyze Project P (Soup).

    Usable veg = 100 * 0.9 = 90 kg.

    Max from veg = (90 / 2) * 10 = 450 liters.

    Available time = 40 - 2 = 38 hours.

    Max from time = 38 * 10 = 380 liters.

    Binding: Time. Max: 380 liters. (Matches 2)

    Step 2: Analyze Project Q (Bread).

    Max from flour = 60 * 5 = 300 loaves.

    Available time = 30 - 1 = 29 hours.

    Rate = 5 loaves / 0.5 hrs = 10 loaves/hr.

    Max from time = 29 * 10 = 290 loaves.

    Binding: Time. Max: 290 loaves. (Matches 4)

    Step 3: Analyze Project R (Rice).

    Max from rice = 50 * 20 = 1000 meals.

    Available time = 20 - 1 = 19 hours.

    Rate = 20 meals / 15 mins = 80 meals/hr.

    Max from time = 19 * 80 = 1520 meals.

    Binding: Ingredient (Rice). Max: 1000 meals. (Matches 1)

    Step 4: Analyze Project S (Dal).

    Max from dal = 45 * 15 = 675 meals.

    Available time = 25 hours.

    Rate = 15 meals / 20 mins = 45 meals/hr.

    Max from time = 25 * 45 = 1125 meals.

    Binding: Ingredient (Dal). Max: 675 meals. (Matches 3)

    Step 5: Combine the matches.

    P-2, Q-4, R-1, S-3.

    Answer: A

    Question 4 · Decision Making (DM) MCQ

    An NGO receives donations of Rice (R) and Lentils (L) to prepare two types of meals: Basic (B) and Premium (P).

    • A Basic meal requires 2 kg of Rice and 1 kg of Lentils. It generates an impact score of 10.
    • A Premium meal requires 1 kg of Rice and 3 kg of Lentils. It generates an impact score of 15.

    The NGO has exactly 100 kg of Rice and 100 kg of Lentils available.

    Due to contractual obligations, they must prepare at least 10 Basic meals and at least 10 Premium meals.

    All meals prepared must be whole numbers.

    Which of the following total impact scores is IMPOSSIBLE to achieve given these constraints?

    1. A.

      700

    2. B.

      690

    3. C.

      695

    4. D.

      680

    Correct Answer:

    C

    Step-by-Step Solution

    Key idea: This is a linear programming feasibility problem (C1T1) with integer constraints. We must find the feasible region and check which target value cannot be formed by integer coordinates within it.

    Step 1: Formulate the constraints.

    Rice:

    Lentils:

    Minimums:

    Objective:

    Step 2: Find the maximum possible impact.

    The maximum occurs at the intersection of the resource constraints:

    Subtracting the first from the second: .

    Then .

    Check minimums: . Valid.

    Max Impact = . (Option A is possible).

    Step 3: Check Option B (690).

    .

    Try .

    Check constraints: . . Valid. (Option B is possible).

    Step 4: Check Option C (695).

    .

    Since is even, must be odd, so must be odd.

    If .

    Check Lentils: . (Fails).

    If .

    Check Rice: . (Fails).

    No integer solution exists near the boundary. (Option C is IMPOSSIBLE).

    Step 5: Check Option D (680).

    . Try .

    Check constraints: . . Valid. (Option D is possible).

    Answer: C

    Question 5 · Decision Making (DM) MCQ

    An NGO has 3 volunteers. They must complete 4 tasks:

    • T1: 2 days, requires 1 volunteer.
    • T2: 3 days, requires 1 volunteer.
    • T3: 2 days, requires 3 volunteers.
    • T4: 4 days, requires 1 volunteer.

    Dependencies:

    • T1 must finish before T3 starts.
    • T2 and T3 must finish before T4 starts.

    Volunteers can be reassigned instantly, but a task cannot be paused once started.

    What is the minimum number of days required to complete all tasks?

    1. A.

      8

    2. B.

      9

    3. C.

      10

    4. D.

      11

    Correct Answer:

    B

    Step-by-Step Solution

    Key idea: This is a decision checklist and scheduling problem with a hidden volunteer constraint. The standard critical path must be adjusted for resource availability.

    Step 1: Find the standard critical path (ignoring volunteer limits).

    Path 1: T1(2) T3(2) T4(4) = 8 days.

    Path 2: T2(3) T4(4) = 7 days.

    Standard critical path = 8 days.

    Step 2: Apply the volunteer constraint.

    T3 requires 3 volunteers. We only have 3 volunteers total.

    This means T3 can only start when ALL 3 volunteers are free.

    Step 3: Schedule the tasks.

    Days 1-2: T1 (V1), T2 (V2). V3 is idle.

    Day 3: T1 is done. T3 needs 3 volunteers, but V2 is still busy with T2 (which takes 3 days).

    So T3 CANNOT start on Day 3. We must wait for T2 to finish.

    Day 4: T2 finishes. Now V1, V2, V3 are all free.

    Days 4-5: T3 (V1, V2, V3). T3 takes 2 days, finishes at the end of Day 5.

    Days 6-9: T4 (V1). T4 takes 4 days, finishes at the end of Day 9.

    Total time = 9 days.

    Answer: 9

    More practice questions in this unit

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    Operations, Social Initiatives and Process Optimization Practice Questions for XAT: 99+ Solved Questions with Step-by-Step Solutions

    Solve 99+ Operations, Social Initiatives and Process Optimization practice questions for XAT with answers and detailed solutions. Free sample questions below.

    A question from this chapter

    Question 1

    In a kitchen scheduling network with multiple paths from start to finish, the critical path is best defined as:

    Question 2

    An NGO kitchen has 1 prep station and 1 stove. They receive a donation of exactly 14 kg of potatoes, which must be fully used to make Aloo Curry (AC) or Aloo Tikki (AT).

    • AC requires 2 kg potatoes, 20 mins prep, 30 mins cook.
    • AT requires 1 kg potatoes, 30 mins prep, 10 mins cook.

    The kitchen must make at least as many AC as AT.

    Preparation for a dish must be completely finished before its cooking can begin. There is no time lost in transferring a dish. The stove can only cook one dish at a time, but the prep station can prep the next dish while the stove is cooking.

    What is the maximum number of meals they can finish cooking within 220 minutes?

    Question 3

    An NGO runs four community kitchen projects (P, Q, R, S), each producing a different meal. The manager needs to identify the binding constraint and the maximum weekly output for each project.

    Project P (Soup): Has 100 kg of vegetables, but 10% is wasted before use. Requires 2 kg of usable veg per 10 liters of soup. Takes 1 hour to cook 10 liters. Has 40 hours/week, but 2 hours are lost to setup.

    Project Q (Bread): Has 60 kg of flour. Requires 1 kg of flour per 5 loaves. Takes 0.5 hours to bake 5 loaves. Has 30 hours/week, but the oven requires 1 hour of preheating before any baking.

    Project R (Rice): Has 50 kg of rice. Requires 1 kg of rice per 20 meals. Takes 15 minutes to cook 20 meals. Has 20 hours/week, but the rice must soak for 1 hour before cooking can begin.

    Project S (Dal): Has 45 kg of lentils. Requires 1 kg of lentils per 15 meals. Takes 20 minutes to cook 15 meals. Has 25 hours/week with no setup or soak times.

    Match each project to its Binding Constraint and Maximum Weekly Output:

    List II:

    1. Ingredient, 1000 meals
    2. Time, 380 liters
    3. Ingredient, 675 meals
    4. Time, 290 loaves
    Question 4

    An NGO receives donations of Rice (R) and Lentils (L) to prepare two types of meals: Basic (B) and Premium (P).

    • A Basic meal requires 2 kg of Rice and 1 kg of Lentils. It generates an impact score of 10.
    • A Premium meal requires 1 kg of Rice and 3 kg of Lentils. It generates an impact score of 15.

    The NGO has exactly 100 kg of Rice and 100 kg of Lentils available.

    Due to contractual obligations, they must prepare at least 10 Basic meals and at least 10 Premium meals.

    All meals prepared must be whole numbers.

    Which of the following total impact scores is IMPOSSIBLE to achieve given these constraints?

    Question 5

    An NGO has 3 volunteers. They must complete 4 tasks:

    • T1: 2 days, requires 1 volunteer.
    • T2: 3 days, requires 1 volunteer.
    • T3: 2 days, requires 3 volunteers.
    • T4: 4 days, requires 1 volunteer.

    Dependencies:

    • T1 must finish before T3 starts.
    • T2 and T3 must finish before T4 starts.

    Volunteers can be reassigned instantly, but a task cannot be paused once started.

    What is the minimum number of days required to complete all tasks?

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