Prof. Templeton had purchased a 1 Km square plot of land. He was told by the Utility Company that their lines pass through his property somewhere, but they didn’t know exactly where they were and if the Prof. wanted to tap into the lines, he was responsible for paying to have them dug down to and determining where they ran through the property. All the Utility Company would tell him for certain was that the lines ran parallel to the ground and traveled in a straight line. So Prof. Templeton asked Doug the digger to come over and give him an estimate on finding the utility lines.

“The cost to dig is $1.00 per meter and I’ll have to dig around the perimeter to find those lines, so that’s four grand”, said Doug.

“I don’t think you need to do that”, said the Prof.

“You’re right. I can just dig around three sides and find those lines”, replied Doug

“You can still do better than that”, said the Prof.

What optimal digging path to find the utility lines did the Prof. have in mind and what is the least it will cost to have Doug dig?

## Question

## Prof. Templeton

Prof. Templeton had purchased a 1 Km square plot of land. He was told by the Utility Company that their lines pass through his property somewhere, but they didn’t know exactly where they were and if the Prof. wanted to tap into the lines, he was responsible for paying to have them dug down to and determining where they ran through the property. All the Utility Company would tell him for certain was that the lines ran parallel to the ground and traveled in a straight line. So Prof. Templeton asked Doug the digger to come over and give him an estimate on finding the utility lines.

“The cost to dig is $1.00 per meter and I’ll have to dig around the perimeter to find those lines, so that’s four grand”, said Doug.

“I don’t think you need to do that”, said the Prof.

“You’re right. I can just dig around three sides and find those lines”, replied Doug

“You can still do better than that”, said the Prof.

What optimal digging path to find the utility lines did the Prof. have in mind and what is the least it will cost to have Doug dig?

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