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Math Help - a- Write the simplex matrix to maximize the profit.

  1. #1
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    a- Write the simplex matrix to maximize the profit.

    Hello:
    I need to Write the simplex matrix to maximize the profit in the following problem:

    A contractor builds two types of homes. The Carolina model requires one lot, $160,000 in capital, and 160 worker-days of labor and the Savannah model requires one lot, $240,000 in capital, and 160 worker-days of labor. The contractor owns 300 lots, has $48,000,000 available capital, and has 43,200 available worker- days of labor. The profit on the Carolina model is $40,000. The profit on the Savannah model is $50,000. Find how many of each type of home should be built to maximize profit.


    my answer is:
    Maximize: F = 40,000x + 50,000y, subject to :
    x + y ≤ 300
    160,000x + 240,000y ≤ 48,000,000
    160x + 160y ≤ 43,200

    is that correct? my textbook tells me that's not correct, I don't understand why.

    thank you.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jhonwashington View Post
    Hello:
    I need to Write the simplex matrix to maximize the profit in the following problem:

    A contractor builds two types of homes. The Carolina model requires one lot, $160,000 in capital, and 160 worker-days of labor and the Savannah model requires one lot, $240,000 in capital, and 160 worker-days of labor. The contractor owns 300 lots, has $48,000,000 available capital, and has 43,200 available worker- days of labor. The profit on the Carolina model is $40,000. The profit on the Savannah model is $50,000. Find how many of each type of home should be built to maximize profit.


    my answer is:
    Maximize: F = 40,000x + 50,000y, subject to :
    x + y ≤ 300
    160,000x + 240,000y ≤ 48,000,000
    160x + 160y ≤ 43,200

    is that correct? my textbook tells me that's not correct, I don't understand why.

    thank you.

    Recheck the question, if what you have type is correct, then the constraint x+y\le  300 is not relevant as 160x + 160y \le 43,200 is always stricter. Also you have not given the non-negativity constraints x \ge 0 and y\ge 0

    CB
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