Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: a type A, x, vessei 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 $58,000 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 =
(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.
≤CM
(c) Find the range of values that Requirement 1 for deluxe cabins can assume. (Requirement 1 pertains to the deluxe cabin requirement.)
< (Requirement 1) ≤
at (x, y) =
(d) Find the shadow price for Requirement 1 for deluxe cabins. (Round your answer to the nearest cent.)
$
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Transcribed Image Text:EY Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: a type A, x, vessei 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 $58,000 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 = (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. ≤CM (c) Find the range of values that Requirement 1 for deluxe cabins can assume. (Requirement 1 pertains to the deluxe cabin requirement.) < (Requirement 1) ≤ at (x, y) = (d) Find the shadow price for Requirement 1 for deluxe cabins. (Round your answer to the nearest cent.) $ Need Help? Read It Watch It
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