Question

Solve in maple if possible.

5. (15 points) One application of linear systems of equations is traffic analysis. Below is a diagram of part of the Inner Harbor area of Baltimore. The problem you want to explore is the amount of traffic among the eight intersections (labeled A, B, H). The arrows indicate the direction of traffic. Each street is a one-way street. The numbers indicate the number of vehicles (per hour) that enters or leaves an intersection. For example, intersection A has x4 plus x7 vehicles entering leaving the intersection. (We will assume that the number of cars entering an intersection is equal to the number of cars leaving the intersection.) the intersection and 300 plus x1 vehicles Calvert St South St Charles St Light St x3 100 x1 x2 C X D 400 Lombard St-300 A x4 B x5 rs x8 Ху x10 x7 Pratt St300 E x11F x12 G x13 H 600 r14 400 500 (a) Set up a linear system that describes the number of cars entering and leaving the eight intersections. (b) Solve the linear system. (c) Interpret your solution in the context of this problem. (Hint: x1, x2,... must be nonnegative. We will interpret a negative number of cars as going the wrong way on the one-way street. For the safety of all, we will not allow negative numbers.)

Answer 1

a) Entering a node the variables are added in the left side and exiting the node are written on the right side and equations are obtained as follows: Thus the linear system is after \r\n Thus the linear system is after Simplifying -X1 + X4 + X7 = 300 X2 - X4 + X5 - X8 = 0 X3 + X5 - X6 - X9 = 0 X6 + X10 = 500 X11 + X7 - X14 = 300 X8 + X11 - X12 = 400 X9 - X12 + X13 = 500 X10 + X13 = 600 \r\n b) Solving by Gauss elimination we can get Solution set: x1 = x4 - x11 + x14 x2 = 400 + x4 - x5 - x11 + x12 x3 = 400 - x5 + x12 x6 = -100 + x13 x7 = 300 - x11 + x14 x8 = 400 - x11 + x12 x9 = 500 + x12 - x13

This can be done by any software,

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