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19 August, 15:06

A craftsman builds two kinds of birdhouses, one for wrens and one for bluebirds. Each wren birdhouse takes 3 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 10 units of lumber. The craftsman has available 80 hours of labor and 100 units of lumber, and he wants to build at least 6 wren houses. Wren houses profit $8 each and bluebird houses profit $16 each. How many of each kind of birdhouses should be built in order to maximize total profit? Formulate this as a linear programming problem (i. e., DO NOT solve it.)

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  1. 19 August, 15:54
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    Obj Function, Max P=8w+16b

    Subject to the Constraints

    3w+2l≤80

    4w+10b≤100

    w≥6

    b>0

    Step-by-step explanation:

    Let the number of Wren's birdhouse built=w

    Let the number of bluebirds birdhouse built=b

    Constraint:Labour

    Each wren birdhouse takes 3 hours of labor.

    Each bluebird house requires 2 hours of labor.

    The craftsman has available 80 hours of labor

    Formulated as an inequality:

    3w+2l≤80

    Constraint: Lumber

    Each wren birdhouse requires 4 units of lumber.

    Each bluebird birdhouse 10 units of lumber.

    The craftsman has available 100 units of lumber

    Formulated as an inequality:

    4w+10b≤100

    The craftsman wants to build at least 6 wren houses.

    w≥6

    Since he builds the two kinds of house, b>0 and w>0.

    Objective Function

    Wren houses profit $8 each and bluebird houses profit $16 each.

    The Objective of the function is to make profit, so we maximize.

    Obj Function, Max P=8w+16b

    The linear programming problem is therefore stated below:

    Obj Function, Max P=8w+16b

    Subject to the Constraints

    3w+2l≤80

    4w+10b≤100

    w≥6

    b>0
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