Proof without words that the three utilities problem has no solution by CMG Lee. The leftmost house is first deleted. The lines connecting the utilities with the remaining houses divide the plane into three regions, shaded yellow, red and blue. Whichever region the deleted house is placed into, one of the utilities is outside the region.


An old, yet ever popular recreational problem is the utilities problem, also known as the water, gas, and electricity problem, which is usually stated as follows: Try to install water, gas, and electrical lines from utilities W, G, and E to each of the houses

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The utilities problem is a mathematical classic - It's impossible to solve it on a flat surface (a plan

This problem comes under the heading of graph theory. You have probably heard of Euler's formula for plane graphs. The classical mathematical puzzle known as the three utilities problem; the three cottages problem or sometimes water, gas and electricity can be stated as follows: Suppose there are three cottages on a plane (or sphere) and each needs to be connected to the gas, water, and electricity companies. Without using a third dimension or sending any of the connections through another company or Three utilities problem: | The classical |mathematical puzzle| known as |water, gas, and electricity|; the |thr World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled.

3 utilities problem

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3 utilities problem

She has an income of 100 and P 1 = 1 and P 2 = 1.

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Whichever region the deleted house is placed into, one of the utilities is outside the region. 3 utilities problem blank: Image title: Three utilities (water, gas and electricity) are to be directly connected to three houses without any connections crossing, as … This also brings up a problem for new competing companies in the utility fields as they find it more and more difficult to add their utility in parkways. To keep the utility fields competitive there will be a need for joint work between the competitors using the same space, such as communications companies share space with underground systems.” CCleaner. As a computer gets older, it collects unused files and settings which take up hard drive … File:3 utilities problem plane.svg. Size of this PNG preview of this SVG file: 512 × 341 pixels.


Since all sales are on cash basis, there is no problem of bad debt losses. Since public utilities are run as monopolies and the goods and services sold by them are indispensable, there is no requirement for a high degree of salesmanship. Problem 2. Consumer’s surplus Suppose Birgitta has the utility function U = x 1 0.1 x 2 0.9. She has an income of 100 and P 1 = 1 and P 2 = 1. Calculate compensating and equivalent variation when the price of x1 increases to 2.

As a result, a utility func-tion exists. We normally assume preferences also satisfy monotonicity (so indifierence curves are well behaved) and convexity (so the optima can be characterised by tangency conditions). The expenditure minimisation problem is min x1;:::;xN XN i=1 3 The Utility Maximization Problem We have now discussed how to describe preferences in terms of utility functions and how to formulate simple budget sets.