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lecture7.5 - Math 006(Applications Example 1 A chemical...

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Math 006 (Applications) Example 1. A chemical manufacturer wants to lease a fleet of 24 railroad tank cars with a combined carrying capacity of 520,000 gallons. Tank cars with three different carrying capacities are available: 8,000 gallons, 16,000 gallons, and 24,000 gallons. How many of each type of tank car should be leased?
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Example 2. The rush-hour traffic flow for a network of for one-way streets in a city is shown in the figure. The numbers next to each street indicate the number of vehicles per hour that enter and leave the network on that street. The variable x 1 , x 2 , x 3 and x 4 represent the flow of traffic between the four intersections in the network. (a) For a smooth traffic flow, the number of vehicles entering each intersection should always equal the number leaving. For example, since 1000 vehicles enter the intersec- tion of 1st Street and 3rd Street each hour and x 1 + x 3 vehicles leave this intersection, we see that x 1 + x 3 = 1000. Find the equations determined by the traffic flow at each of the other three intersections.
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