(U3.3,Q3) Airbus A330-300s seat 330 passengers and cost $250 million each, Boeing 767-300ERs seat 270 passengers and cost $200 million each, while Boeing Dreamliner 787-9s seat 240 passengers and cost $250 million each. You are the purchasing manager of an airline company and have a spending goal of $5550 million for the purchase of new aircraft to seat a total of 6750 passengers. Your company has a policy of supporting U.S. industries, and you have been instructed to buy twice as many Boeings as Airbuses. Given the selection of three aircraft, how many of each should you order of each? Airbus A330-300s ______Boeing 767-300ERs ______ Boeing Dreamliner 787-9s ______

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Asked Dec 15, 2019
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(U3.3,Q3)
 
Airbus A330-300s seat 330 passengers and cost $250 million each, Boeing 767-300ERs seat 270 passengers and cost $200 million each, while Boeing Dreamliner 787-9s seat 240 passengers and cost $250 million each. You are the purchasing manager of an airline company and have a spending goal of $5550 million for the purchase of new aircraft to seat a total of 6750 passengers. Your company has a policy of supporting U.S. industries, and you have been instructed to buy twice as many Boeings as Airbuses. Given the selection of three aircraft, how many of each should you order of each?
 
Airbus A330-300s ______
Boeing 767-300ERs ______ 
Boeing Dreamliner 787-9s ______
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Expert Answer

Step 1

Find number of three aircraft.

Let x be the number Airbus, y be the number of Boeing and z be the Boeing Dreamliner.

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Conditions: Airbus has 330 passengers seat and cost $250 million. Boeing has 270 passengers seat and cost $200 million. Boeing Dreamliner has 240 passengers seat and cost $250 million. Purchasing the aircraft of 6750 passengers with a total cost of $5550 million.

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Step 2

Thus, write these data in equation form.

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330x+270y+240z=6750 -…-(1) 250x+200y+250z=5550 .-(2) Condition to buy twice as many Boeings as Airbuses y+z=2x 2x– y-z=0 ..(3)

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Step 3

Solve three equations, ...

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From equation (1), 330x+270y+240z=6750 Divide by 30, 225-9y-8z х 11 From equation (2), 250x+200y+250z=5550 Divided by 50, 5x +4y+5z =111 ´225-9y-8z +4y+5z=111 5 11 y=-3(-5z+32)

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