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Math Help - linear systems problem

  1. #1
    Senior Member euclid2's Avatar
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    linear systems problem

    Doug, Marilyn and Tran are to provide advice on the suppliers for hamburgers for the food court. Isosceles Foods charges a delivery fee of $52.50 and $1.10 for each hamburger. Scalene Wholesale charges a delivery fee of $12.30 and $1.17 for each hamburger.

    1. Determine the cost of purchasing 200 hamburgers from each company.
    2. Determine the cost of purchasing 2000 hamburgers from each company.
    3. If cost is the main concern, describe the circumstances under which each company should be selected
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  2. #2
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    Quote Originally Posted by euclid2 View Post
    Doug, Marilyn and Tran are to provide advice on the suppliers for hamburgers for the food court. Isosceles Foods charges a delivery fee of $52.50 and $1.10 for each hamburger. Scalene Wholesale charges a delivery fee of $12.30 and $1.17 for each hamburger.

    1. Determine the cost of purchasing 200 hamburgers from each company.
    2. Determine the cost of purchasing 2000 hamburgers from each company.
    3. If cost is the main concern, describe the circumstances under which each company should be selected
    For every x number of humbergers delivered, in dollars,
    >>>Isosceles Food: Cost, Ci = 52.50 +1.10x
    >>>Scalene Wholesale; Cost, Cs = 12.30 +1.17x

    [*]Determine the cost of purchasing 200 hamburgers from each company.
    Ci = 52.50 +1.10*200 = 272.50 dollars
    Cs = 12.30 +1.17*200 = 246.30 dollars ....less than Ci

    [*]Determine the cost of purchasing 2000 hamburgers from each company.
    Ci = 52.50 +1.10*2000 = 2,252.50 dollars
    Cs = 12.30 +1.17*2000 = 2,352.30 dollars ....more than Ci

    [*]If cost is the main concern, describe the circumstances under which each company should be selected
    This is the purpose of this exercise. It is about linear systems, specifically, about two linear equations of differing slopes.
    Ci = 52.50 +1.10x can be viewed in the form y = mx +b as
    Ci = (1.10)x +52.50 ------(1)

    Likewise, Cs = (1.17)x +12.30 -----(2)

    The slope of Cs, (1.17), is steeper or "greater" than the slope of Ci, (1.10).
    So although Cs starts lower or cheaper than Ci for lesser x humburgers delivered, eventually Cs will be greater or costlier than Ci for more or bigger number of x humburger delivered.
    You can graph the Ci and Cs on the same (x,y) axes and you will see that they will intersect at some x humburger delivered. At this intersection, Ci and Cs are the same or equall in costs. Before that intersection, the Cs is cheaper. After that intersection, the Cs is costlier.
    So, if cost is the main concern, buy humburgers from Scalene Wholesale if the x number of humburger to be delivered is less than that x number at the intersection point. Otherwise, buy from Isosceles Food.

    Geez, I talk too much. What that all means is equate Ci and Cs. Find the x when Ci and Cs are equal.
    Ci = 52.50 +1.10x
    Cs = 12.30 +1.17x

    Ci minus Cs,
    (Ci -Cs) = 40.20 -0.07x
    When Ci = Cs,
    0 = 40.20 -0.07x
    0.07x = 40.20
    x = 40.20 / 0.07
    x = 574.3 humbergers delivered.

    Therefore, for 574 or less humburgers, buy from Scalene Wholesale. For 575 or more humburgers, buy from Isosceles Food.
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