Radiant wants to hire Cargo planes for transporting their goods. They contacted
ID: 423174 • Letter: R
Question
Radiant wants to hire Cargo planes for transporting their goods. They contacted VIP Transportation Company to hire Cargo planes. VIP informed that they can provide two types of Cargo Planes. In addition, they provided the following cost related information about the two types Cargo planes- WT88 and BH54:
Personnel Cost
Fuel Cost
Maintenance Cost
WT88
2000
1000
2000
BH54
2500
1500
1000
Radiant has $20,000 to spend in personnel cost, $6000 in fuel cost, and $8000 in maintenance cost. If WT88 can carry 45 tons of goods and BH54 can carry 65 tons of goods then find out the following:
A) What is the maximum amount Radiant can carry given their budget constraint?
B) To carry the maximum amount how many of WT88 and BH54 radiant should hire.
Personnel Cost
Fuel Cost
Maintenance Cost
WT88
2000
1000
2000
BH54
2500
1500
1000
Explanation / Answer
Given,
WT88 can carry 45 tons of goods
and
BH54 can carry 65 tons of goods
Let the number of WT88 that would be used be x
and
the number of BH54 that would be used be y
Therefore, the constraint equations are:
2000*x + 2500*y <= 20000 (Personnel Cost)
1000*x + 1500*y <= 6000 (Fuel Cost)
2000*x + 1000*y <= 8000 (Maintenance Cost)
From the above equations, we can say that the maximum vale that is possible for x is 4 when y is 0 and y is 4 when x is 0, satisfying these equations. Hence, there are various matrix of combination of x and y are possible, but we need to find the one which returns us the maximum amount.
When x=3, y=2 we get the maximum amount as 45*3 + 65*2 = 265 (this also satisfies all the constraint equations).
Hence,
A) The maximum amount that Radiant can carry given their budget constraint is 265 tons.
B) To carry the maximum amount, 3 WT88 and 2 BH54 should be hired by Radiant.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.