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Problem 12

TraNSPoRTATION 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 \(\$ 44,000\) to operate a type-A vessel and \(\$ 54,000\) to operate a type-B vessel for that period. How many of each type vessel should be used in order to keep the operating costs to a minimum?

Expert verified

The graph of the constraints shows a feasible region with three corner points: (4, 3), (6, 1.5), and (0, 8.5). Evaluate the objective function at each corner point:
1. Corner point 1: C(4, 3) = 44,000(4) + 54,000(3) = \$302,000
2. Corner point 2: C(6, 1.5) = 44,000(6) + 54,000(1.5) = \$312,000
3. Corner point 3: C(0, 8.5) = 44,000(0) + 54,000(8.5) = \$459,000
The minimum cost is \$302,000, which occurs when 4 type-A vessels and 3 type-B vessels are used.

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