Chapter 11, Problem 53AP

(a)

Summary Introduction

Interpretation: Frank Green, an independent RV repairman, is considering purchasing a home in Ames, Iowa, that he will use as a base of operations for his repair business. Frank’s primary sources of business are 10 industrial accounts located throughout the Ames area. He has overlaid a grid on a map of the city and determined the following locations for these clients as well as the expected number of calls per month he receives as given in the tabulation. Assuming a weighted rectilinear distance measurement, the optimal location of his house needs to be determined.

Client	Grid Location	Expected Calls per Month.
1	(5,8)	2
2	(10,3)	1
3	(14,14)	1
4	(2,2)	3
5	(1,17)	1
6	(18,25)	1/2
7	(14,3)	1/4
8	(25,4)	4
9	(35,1)	3
10	(16,21)	1/6

Concept Introduction: When the differences between the $x\text{ and }y$ coordinates are added, then it gives the Recti-linear distance between two points along an orthogonal path.

(b)

Summary Introduction

Interpretation: Frank Green, an independent RV repairman, is considering purchasing a home in Ames, Iowa, that he will use as a base of operations for his repair business. Frank’s primary sources of business are 10 industrial accounts located throughout the Ames area. He has overlaid a grid on a map of the city and determined the following locations for these clients as well as the expected number of calls per month he receives as given in the tabulation. Assuming a squared Euclidean distance measurement, the optimal location of his house needs to be determined.

Client	Grid Location	Expected Calls per Month.
1	(5,8)	2
2	(10,3)	1
3	(14,14)	1
4	(2,2)	3
5	(1,17)	1
6	(18,25)	1/2
7	(14,3)	1/4
8	(25,4)	4
9	(35,1)	3
10	(16,21)	1/6

Concept Introduction: The simple measurement of distance in a straight line between two facilities is called Euclidean Distance.

(c)

Summary Introduction

Interpretation: Frank Green, an independent RV repairman, is considering purchasing a home in Ames, Iowa, that he will use as a base of operations for his repair business. Frank’s primary sources of business are 10 industrial accounts located throughout the Ames area. He has overlaid a grid on a map of the city and determined the following locations for these clients as well as the expected number of calls per month he receives as given in the tabulation. Assuming the goal is to minimize the maximum rectilinear distance to any client, the optimal location of his house needs to be determined.

Client	Grid Location	Expected Calls per Month.
1	(5,8)	2
2	(10,3)	1
3	(14,14)	1
4	(2,2)	3
5	(1,17)	1
6	(18,25)	1/2
7	(14,3)	1/4
8	(25,4)	4
9	(35,1)	3
10	(16,21)	1/6

Concept Introduction: Rectilinear Distance: When the distance between two facilities are measured in an orthogonal path, then it is called a rectilinear distance