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Question 1021254: Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 45 deluxe cabins and 155 standard cabins, whereas a type-B vessel has 80 deluxe cabins and 110 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 455 deluxe and 905 standard cabins for their 15-day cruise in May. It costs $40,000 to operate a type-A vessel and $52,000 to operate a type-B vessel for that period. How many of each type of vessel (x type-A and y type-B) should be used in order to keep the operating costs to a minimum, C?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Deluxe River Cruises operates a fleet of river vessels.
The fleet has two types of vessels:
A type-A vessel has 45 deluxe cabins and 155 standard cabins, whereas
a type-B vessel has 80 deluxe cabins and 110 standard cabins.
Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 455 deluxe and 905 standard cabins for their 15-day cruise in May.
:
Find the exact number of vessels required to meet these requirement
The deluxe cabin equation
45x + 80y = 455
Standard cabin equation
155x + 110y = 906
Use elimination with these two equations,
multiply the 1st equation by 11,
multiply the 2nd equation by 8
Subtract the 1st equation from the 2nd equation
1240x + 880y = 7240
495x + 880y = 5005
--------------------subtracting eliminates y, find x
745x + 0 = 2235
x = 2235/745
x = 3 ea type A ships
:
Find y
45(3) + 80y = 455
80y = 455 - 235
y = 320/80
y = 4 ea type B ships
It costs $40,000 to operate a type-A vessel and $52,000 to operate a type-B vessel for that period.
Cost = 3(40000) + 4(52000)
C = $320,000 total cost
:
How many of each type of vessel (x type-A and y type-B) should be used in order to keep the operating costs to a minimum, C?
3 type A, 4 type B, any other combination requires more than 7 ships
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