Question

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

Answer 1

9 Airbus planes, 1 Boeing plane & 4 Lockheed airplanes

Step-by-step 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