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24 June, 06:45

A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 hours respectively. The employee hours available in a month are 1,500 for the welding department, 1,500 in assembly and 550 in painting. The contribution to profits are 100 USD for product X and 120 USD for product Y. What is the objective function (Z) to be maximised in this linear programming problem (where Z is total profit in USD) ? (note : means = )

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  1. 24 June, 08:37
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    100x+120y = z

    z = $ 63000

    Step-by-step explanation:

    Product Welding Assembly Painting Cont. to profit

    X 2x hours 3x hours 1xhour = $100x

    Y 3y hours 2y hours 1y hour = $120y

    Total hours 1500 hours 1500 hours 550 hours

    available

    Let X represent product X

    Let Y represent Product Y

    2x + 3y = 1500

    x + y = 550

    y = 550-x

    2x + 3 (550-x) = 1500

    2x + 1650 - 3x = 1500

    150 = x

    y = 550-150

    y = 400

    Objective Function Z = 100x + 120y

    Z = 100 (150) + 120 (400)

    Z = 15000+48000

    Z = $63000
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