Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: a type A, x, vessel has 60 deluxe cabins and 160 standard cabins, whereas a type B vessel, y, has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with the 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 $44,000 to operate a type A vessel and $54,000 to operate a type B vessel for that period. (a) How many of each type of vessel should be used to keep the operating costs C to a minimum? The minimum is C = ______at (x, y) =(_____). (b) Suppose C = cx + 54,000y. Find the range of values that the cost of operating a type A vessel, the coefficient c of x, can assume without changing the optimal solution. _____≤ c ≤_____ (c) Find the range of values that Requirement 1 for deluxe cabins can assume. (Requirement 1 pertains to the deluxe cabin requirement.)_____ ≤ (Requirement 1) ≤_____ (d) Find the shadow price for Requirement 1 for deluxe cabins. (Round your answer to the nearest cent.) $_____
Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: a type A, x, vessel has 60 deluxe cabins and 160 standard cabins, whereas a type B vessel, y, has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with the 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 $44,000 to operate a type A vessel and $54,000 to operate a type B vessel for that period.
(a) How many of each type of vessel should be used to keep the operating costs C to a minimum? The minimum is C = ______at (x, y) =(_____).
(b) Suppose C = cx + 54,000y. Find the range of values that the cost of operating a type A vessel, the coefficient c of x, can assume without changing the optimal solution. _____≤ c ≤_____
(c) Find the range of values that Requirement 1 for deluxe cabins can assume. (Requirement 1 pertains to the deluxe cabin requirement.)_____ ≤ (Requirement 1) ≤_____
(d) Find the shadow price for Requirement 1 for deluxe cabins. (Round your answer to the nearest cent.) $_____
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