Question

An airline has been tasked with repatriating SA citizens who are currently stranded in Europe due to the Covid 19 crisis. The airline has been given a budget of R3.5 million rands by donors for fuel to transport 12 000 passengers. The airline has 2 types of aircraft, a large and smaller one. The fuel costs for a return flight are R145 000 and R85 000 respectively. The labour hours for each return flight are 12 hours for the large plane and 8 for the small with a total of 300 hours budgeted for the month. (The labour budget is not part of the fuel budget). The large plane can transport 650 passengers while the smaller one can transport 350 passengers. Due to the urgency of the matter, each type of plane must make at least 10 trips to Europe.

You are required to use Solver on excel to answer the questions that follow.

1. How many return trips should each type of aircraft make in order to bring home the 12 000 passengers while minimizing fuel costs and the hours for the month?

Large aircraft   return trips.

Small aircraft   return trips.

2. How much of the fuel budget would not be used? R

3. How many crew hours would be left for the month? : hours

Before any flights have embarked on the mission, it has been discovered that an additional 1500 SA citizens have indicated their desire to return home. How many trips would be required now given this increase in passenger numbers?

Large aircraft :

Small aircraft:

How much of the fuel budget would not be spent? R

Hours that would not be used: hours

Given that 13500 passengers need to be transported and that the government would like to substitute the smaller plane for a medium sized plane that can carry 450 passengers with fuel costs of R100 000 per return flight. Labour hours would be the same as the small aircraft.

How many flights would be taken then by the large and medium aircrafts? (Assume no restriction on the number of flights each aircraft can make)

Large : trips

Medium: trips

How much of the fuel budget would remain unused? R

Hours that would not be used: hours

Answer 1

Ans.1 Larger Plane 12 times and smaller trips 12 times (for calculation plz see exel attachment)

1.2million of fuel budget hs not been used

60 hours of remining budget is not used out of 300.

Labour hour for each return flights:-

Large Plane=12 hours

Small Plane=8 hours

Condition:- Each type of plane must take at least 10 trips to europe

Airline has been given a budget of 3500000 rand for fuel to transport 12000 passenger

SOLUTION

Fuel cost for Large plane for 10 compulsury flight:-

145000 multyply 10=1450000

Ten thousand (10000) passanger evacuated in cumpulsory 10 trip (including both plane for 10 trip each)

Labour hour for 10 trip = 12 multyply 10=120

Passaenger carried 650 multiply 10=6500

Total Labour hours spend for this 10 compulsory trip for both plane =120+80=200

For remaining 2000 passenger which is (12000-10000=2000)

Fuel cost for smaller plane for 10 compulsury trip:-

Combination of two large plane and two small plane is sufficient

85000multyply 10=850000

Large Plane-650Multiply2=1300

Labour hours used 12 multiply2=24

Labour hour for 10 trip = 8 multiply 10=80

Smaller Plane-350Multiply2=700

Labour hour used 8*2=16

Passanger carried 350 multiply 10 =350

Total=2000

Total Labour hour used for both plane=200+24+16=240

So remain labour hours would be 300-240=60 hours

Total fuel budget used 1450000+850000=2300000

So remaining unused fuel budget is 3500000-2300000=1200000