Deluxe River Cruises operates a fleet of river vessels The f

Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins and 160 standard cabins, whereas a type-B vessel has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15-day cruise in May. It costs $49,000 to operate a type-A vessel and $56,000 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?

Solution

solution

x= A vessel used

y= B vessel used

c= 49000x+56000y

60x+80y=360= (6x+8y=36)*3 =18x+24y=108 (1)

160x+120y=680= (16x+12y=68)*2= 32x+24y=136 (2)

substract eq 1 from eq 2

14x=28

x=2

y= 3

c= 49000*2+56000*3

c= 98000+168000= 266000

minimum cost= 2,66,000

2 type A, 3 type B, any other combination requires more than 5 ships