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Math Help - Inequalities Problem..

  1. #1
    Junior Member
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    Inequalities Problem..

    This question really stumpted me><...i am really confused, can anyone help me?

    Production Choices: The following system of inequalities models the restrictions on the number x of wooden table chairs and the number y of wooden rocking chairs made at a furniture factory each week. These restrictions are caused by limitations on the factory's equipment and labor supply

    x>0
    y>0
    x+y<50
    3x+y<90

    **All the greater and less than signs are "equal" so, for the first one it's x is greater than and equal to 0. (i dont know how to do the mathematical sign)**

    a) Determine each corner point of the region formed by graphing this system of inequalities.
    b) The factory makes $20 for each table chair and $25 for each rocking chair. Write an expression for the priofit involving x and y
    c) Evaluate the profit expression from part b at each of the corner points from part a. Which of these points produces the greates profit for the factory?
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  2. #2
    MHF Contributor
    Joined
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    x >= 0 ------------(1)
    y >= 0 ------------(2)
    x+y <= 50 ---------(3)
    3x+y <= 90 --------(4)

    a) Determine each corner point of the region formed by graphing this system of inequalities.

    There are four inequalities so there should be four corner points.
    P1 = intersection of inequalities (1) and (2) = (0,0)
    P2 = intersection of inequalities (2) and (3) = (0,50)
    P3 = intersection of inequalities (3) and (4) = (20,30)
    P4 = intersection of inequalities (4) and (1) = (30,0)

    b) The factory makes $20 for each table chair and $25 for each rocking chair. Write an expression for the priofit involving x and y

    P = x(20) +y(30)
    P = 20x +30y --------------in dollars.

    c) Evaluate the profit expression from part b at each of the corner points from part a. Which of these points produces the greates profit for the factory?

    In P1 (0,0)-----P = 20(0) +30(0) = 0
    In P2 (0,50)----P = 20(0) +30(50) = $1500
    In P3 (20,30)---P = 20(20) +30(30) = 400 +900 = $1300
    In P4 (30,0)---P = 20(30) +30(0) = $600

    The point (0,50) produces the greatest profit.
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