A television set manufacturing firm has to decide on the mix of color and black-and-white TVs to be produced. A market research indicates th

Question

A television set manufacturing firm has to decide on the mix of color and black-and-white TVs to be produced. A market research indicates that, at most, 2000 units and 4000 units of color and black-and-white TVs can be sold per month. The maximum number of man-hours available is 60,000 per month. A color TV requires 20 man-hours and a black-and-white TV requires 15 man-hours to manufacture. The unit profits of the color and black-and-white TVs are $60 and $30, respectively. It is desired to find the number of units of each TV type that the firm must produce in order to maximize its profit. Formulate the problem as a linear program.

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Eden 2 weeks 2021-11-19T14:47:30+00:00 1 Answer 0 views 0

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    2021-11-19T14:48:37+00:00

    Answer:

    Objective Function,  Max P =60c+30b

    Subject to the Constraints

    0<c\leq 2000

    0<b\leq 4000

    20c+15b\leq 60000

    Step-by-step explanation:

    Let the number of black t.v. produced =b

    Let the number of colored t.v. produced =c

    at most, 2000 units of color t.v. can be sold i.e. c\leq 2000

    at most 4000 units of black-and-white TVs can be sold i.e. b\leq 4000

    Total man hours per product = Number of Units X Man Hour Per Unit

    A color TV requires 20 man-hours  = 20c

    A black-and-white TV requires 15 man-hours =15b

    Since Maximum number of man Hours is 60000 hours

    20c+15b\leq 60000

    The unit profits of the color TV is $60, therefore total profit =60c

    The unit profits of the black-and-white TVs $30, respectively, therefore total profit =30b

    Since we are to maximize profit, the Objective Function, Max P =60c+30b

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