## Tuesday, August 5, 2014

### Transmit Electricity with Minimum Loss from the Power Plant to the Cities

In this programming assignment, we shall work on finding the shortest path to reach a point on the XY plane. We shall then write a program for Pro-Bot to travel along the shortest path that we found. This is a peek into the world of optimization, comparing and contrasting various solutions to a problem and choosing the best one that fits our needs and constraints.

Your task is to find the paths to the various points on the XY plane, given the XY coordinates. Next, compare and contrast the cost options for the different paths and choose the best one that meets the constraints. Once you have found the best option, determine the  distances and angles at which Pro-Bot has to make turns, in order to traverse the path and write your program.

Computer Science Concepts involved:   Sequential programming, Optimization

Math concepts involved:   Right triangles, Coordinates on XY plane, Measuring distances between points given (x, y) coordinates, Angles,  Finding shortest paths

Grade levels:   4, 5

Hours required:   1

### Programming Assignment

Electricity is generated in power stations and then it gets transported to various cities for distribution to the consumers. Not all of the electricity that gets generated will reach the consumer. Several losses occur along the way on the distribution network. The power company would like to keep the distribution losses at a minimum as the consumers do not pay for it.

Here is a set of coordinates given, representing 3 cities X, Y and Z and the power generation station at point A.

Power is generated at location A and then transported to the cities. For each unit of distance between the points, 1 Kilowatt-hour of energy is lost (Kilowatt-hour is a unit  used to measure energy). Your task is to find the best option for drawing electric lines between the power station and the cities, which will have minimum total loss of electric power during transmission.

Your options are:
(a) to have direct power lines drawn from A to the cities separately or
(b) draw power lines from A to a city and then draw more power lines from that city to the next and so on.

Given the coordinates of the cities and the power station, can you find the shortest distances between them? Use the values that you found to calculate the amount of electrical energy that is lost during transmission to the various cities. Which option do you think would work better, option (a) or option (b) as given above?

Compare all options to see which approach can minimize the total loss of power during transmission from the power station A to all three cities X, Y and Z.

If Pro-Bot is driving along the path that provides the minimum loss of electricity, starting from point A and visiting all three cities, can you write a program to trace Pro-Bot’s path? Assume that Pro-Bot is at the point (0, 0) and facing the X axis when it starts its journey.