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    Group B 3 Assignment 1

    Uploaded by

    YASH MAKADIYA
    The document summarizes two optimization problems solved by Group B-3. The first problem is for a delicatessen that must determine how many fish-n-fowl and surf-n-turf sandwiches to make to maximize profits given ingredient supply constraints. The optimal solution is to make 520 fish-n-fowl sandwiches and 150 surf-n-turf sandwiches. The second problem is for a power plant that must determine how much hard coal and soft coal to use to minimize costs while meeting a power output target and satisfying emission and equipment constraints. The optimal solution determines the amounts of each coal that minimize costs while meeting all constraints.

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    Group B 3 Assignment 1

    Uploaded by

    YASH MAKADIYA
    17 views6 pages
    The document summarizes two optimization problems solved by Group B-3. The first problem is for a delicatessen that must determine how many fish-n-fowl and surf-n-turf sandwiches to make to maximize profits given ingredient supply constraints. The optimal solution is to make 520 fish-n-fowl sandwiches and 150 surf-n-turf sandwiches. The second problem is for a power plant that must determine how much hard coal and soft coal to use to minimize costs while meeting a power output target and satisfying emission and equipment constraints. The optimal solution determines the amounts of each coal that minimize costs while meeting all constraints.

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    The document summarizes two optimization problems solved by Group B-3. The first problem is for a delicatessen that must determine how many fish-n-fowl and surf-n-turf sandwiches to make to maximize profits given ingredient supply constraints. The optimal solution is to make 520 fish-n-fowl sandwiches and 150 surf-n-turf sandwiches. The second problem is for a power plant that must determine how much hard coal and soft coal to use to minimize costs while meeting a power output target and satisfying emission and equipment constraints. The optimal solution determines the amounts of each coal that minimize costs while meeting all constraints.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    17 views6 pages

    Group B 3 Assignment 1

    Uploaded by

    YASH MAKADIYA
    The document summarizes two optimization problems solved by Group B-3. The first problem is for a delicatessen that must determine how many fish-n-fowl and surf-n-turf sandwiches to make to maximize profits given ingredient supply constraints. The optimal solution is to make 520 fish-n-fowl sandwiches and 150 surf-n-turf sandwiches. The second problem is for a power plant that must determine how much hard coal and soft coal to use to minimize costs while meeting a power output target and satisfying emission and equipment constraints. The optimal solution determines the amounts of each coal that minimize costs while meeting all constraints.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 6

    Group B-3

    ASSIGNMENT-1
    BY Group B-3:
    Aasim Ahmad
    Anasuya Chaudhari
    Muskan Kedia
    Rashmi Ranjan Pattanaik
    Yash Makadiya

    1. Delectation Delicatessen
    [Part-A]
    Decision Variables:
    F = Fish-n-fowl sandwich
    S = Surf-n-turf sandwich

    Objective Function:
    Maximum sandwiches: (5.50 * F) + (6.95 * S)

    Supply Constraints:

    (Tuna Fish Salad) (0.25 * F) + (0.25 * S) ≤ 200 …(in pounds)


    (Sliced Roasted Beef) (0 * F) + (0.40 * S) ≤ 60 …(in pounds)
    (Sliced Turkey) (0.5 * F) + (0 * S) ≤ 260 …(in pounds)
    (Rye Bread Slice) (2 * F) + (1 * S) ≤ 1,500 that is; (60*25) …(slices)
    (Pumpernickel Bread Slice) (1 * F) + (1 * S) ≤ 800 that is; (32*25) …(slices)

    Order Constraints:
    Since we need to maximize profits by increased sales, the constraints would be
    F => 0
    S => 0

    Page | 1
    Group B-3

    [Part-B]

    Page | 2
    Group B-3

    Therefore, Delectation should sell 520 Fish-n-Fowl and 150 Surf-n-Turf sandwiches to
    maximize their profits.

    Page | 3
    Group B-3

    2. Power Plant Problem


    [Part-A]
    Decision Variables:
    H = Hard Coal
    S = Soft Coal

    Objective Function:
    Maximum Power Output (BTU): (24000 * H) + (20000 * S)

    Supply Constraints:

    (SO2 Gas Output) (1800 * H) + (3800 * S) ≤ 3300 * (H+S) …(in PPM)


    (Particulate Output) (0.65 * H) + (1.05 * S) ≤ 12 …(in Kilogram)
    (Conveyor Belt) (H + S) ≤ 20 …(in Tons)
    (Pulverizer)
    Since 16 tons per hour of hard coal or 24 tons of soft coal per hour make the pulverizer work
    at 100% output, we remove the percentage of the occupancy of each coal in percentage that
    is,
    For Hard Coal: 1/16 = 0.0625
    For Soft Coal: 1/24 = 0.04117

    For the Linear Equation we plot the points in the first quadrant as follows:

    Using formula:
    x/a + y/b ≤ 1
    (H/16) + (S/24) ≤ 1
    (3*H) + (2*S) ≤ 48
    (Pulverizer) (3*H) + (2*S) ≤ 48 …(in units)

    Page | 4
    Group B-3

    Page | 5
    Group B-3

    [Part-B]
    Decision Variables:
    H = Hard Coal
    S = Soft Coal

    Objective Function:
    Let price of Soft Coal be $100 and so price of Hard Coal will be $115 (1.15*100)
    Cost Minimum: 100*S + 115*H

    Supply Constraints:

    (SO2 Gas Output) (1800 * H) + (3800 * S) ≤ 3300 * (H+S) …(in PPM)


    (Particulate Output) (0.65 * H) + (1.05 * S) ≤ 12 …(in Kilogram)
    (Conveyor Belt) (H + S) ≤ 20 …(in Tons)
    (Pulverizer) (3*H) + (2*S) ≤ 48 …(in units)
    Power Output (BTU) (24000*H) + (20000*S) = 390000 …(in BTU)
    Non-negative constraints: H,S ≥ 0

    Page | 6

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