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1 December, 23:29

Consider the following three types of airplanes: Airbus planes that seat 320 passengers and cost $200 million each, Boeing planes that seat 250 passengers and cost $125 million each, and Lockheed planes that seat 275 passengers and cost $200 million each. You are the purchasing manager of an airline company and have a spending goal of $2,900 million for the purchase of new aircrafts to seat a total of 4,480 passengers. Also, you must buy twice as many Lockheed airplanes as Airbus planes. How many of each type of airplane should you order

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  1. 2 December, 02:04
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    9 Airbus planes, 1 Boeing plane & 4 Lockheed airplanes

    Explanation:

    We will develop equations from the information provided

    Let the planes be tagged as seen below:

    Airbus = x, Boeing = y, Lockheed = z

    From the cost of the planes, we have:

    200 x + 125 y + 200 z = 2900 - --Eqn 1

    From the number of passenger seats, we have:

    320 x + 250 y + 275 z = 4480 - --Eqn 2

    Twice as many Lockheed airplanes as Airbus planes

    ⇒ 2z = x - --Eqn 3

    Substitute x = 2z into Eqn 1, we have:

    200 (2z) + 125 y + 200 z = 2900

    125 y + 400 z + 200 z = 2900

    125 y + 600 z = 2900 - --Eqn 4

    Substitute x = 2z into Eqn 2, we have:

    320 (2z) + 250 y + 275 z = 4480

    250 y + 640 z + 275 z = 4480

    250 y + 915 z = 4480 - --Eqn 5

    Multiply Eqn 4 by 2

    125 y * 2 + 600 z * 2 = 2900 * 2

    ⇒ 250 y + 1200 z = 5800 - --Eqn 6

    (250 y + 915 z = 4480) - --Eqn 5

    Subtracting Eqn 5 from Eqn 6, we have:

    250 y - 250 y + 1200 z - 915 z = 5800 - 4480

    285 z = 1320

    z = 4.6

    Substitute z to Eqn 3, x = 2z

    ⇒ x = 2 * 4.6 = 9.2

    x = 9.2

    Substitute x & z into Eqn 1

    200 x + 125 y + 200 z = 2900

    200 * 9.2 + 125 y + 200 * 4.6 = 2900

    125 y = 2900 - (1840 + 920)

    125 y = 140

    y = 1.1

    Since it is airplanes that are to be bought, the value of x, y & z must be integers (you cannot buy 4.6 airplanes). As such, we will round down values of airplanes to be bought sodo that we will not exceed the budget.

    x = 9, y = 1, z = 4

    ∴That implies that I will buy 9 Airbus planes, 1 Boeing plane & 4 Lockheed airplanes
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