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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Purchasing Aircraft Refer to Exercise 7. Rene’ DuFleur has just been appointed the new CEO of your airline, and you have received instructions that the company policy is now to purchase as many Airbuses as Boeings. Further, the desired seating capacity has been revised downward to 2,910 passengers, and the cost target has been lowered to $2,400 million. Given the specifications of the three types of aircraft, how many of each should you order?

To determine

To calculate: The number of aircraft of each of the three categories should be ordered. The spending goal of the airline company is $2400million and the mission is to seat a total of 2910 passengers. Airbus A330-300s seats 330 passengers and cost $250million each, Boeing767-300ERs seats 270 passengers and cost $200million each while Boeing Dreamliner 787-9s seat 240 passengers and cost $250 million each. According to your company policy, you have to buy Boeings as many Airbuses.

Explanation

Given Information:

The spending goal of the airline company is $2400million and the mission is to seat a total of 2910 passengers.

Airbus A330-300s seats 330 passengers and cost $250million each, Boeing767-300ERs seats 270 passengers and cost $200million each while Boeing Dreamliner 787-9s seat 240 passengers and cost $250 million each.

Also, according to your company policy, you have to buy Boeings as many as Airbuses.

Formula Used:

Elimination method:

In this method, we first combine the equations in a way such that one of the variables gets eliminated. Then we substitute this obtained value in either of the equation to get the value of the other variable.

Calculation:

Let the number of aircraft of each category Airbus A330-300s, Boeing767-300ERs, and Boeing Dreamliner be x,y,z respectively.

It is given that Airbus A330-300s seats 330 passengers and cost $250million each, Boeing767-300ERs seats 270 passengers and cost $200million each while Boeing Dreamliner 787-9s seat 240 passengers and cost $250 million each.

And the mission is to spend $2400 million and seat 2910 passengers.

From the above-mentioned data equations can be formed:

According to the cost of each aircraft,

250x+200y+250z=2400

Simplify the above equation by taking common 50 from each side,

50(5x+4y+5z)=50(48)5x+4y+5z=48 …… (1)

According to seats of each aircraft,

330x+270y+240z=2910

Simplify the above equation by taking common 30 from each side,

30(11x+9y+8z)=30(97)11x+9y+8z=97 …... (2)

The condition says that you have to buy Boeings as many as Airbuses.

Thus, to satisfy the above policy.

y+z=xx+y+z=0 …… (3)

Apply the elimination method to find the solution of the given system of the equations:

Begin by multiplying the third equation with 4 and subtracting it from the first equation to eliminate y.

5x+4y+5z4(x+y+z)=48(5+4)x+(44)y+(54)z=489x+z=48z=489x …… (4)

Now multiplying third equation with 8 and subtracting it from the second equation to eliminate z

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