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

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

1) the stages a new product goes through from beginning to end, i.e., the stages that a product passes through from introduction through growth, maturity, and decline. 2) the time from initial research and development to the time at which sales and support of the product to customers are withdrawn. 3) the period of time during which a product can be produced and marketed profitably.

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