Reference no: EM13961728
Linear Programming - Max Cover
DixieNet is an Internet service provider for residential customers in a southern state. The company is small now but plans to expand. Its first major goal is to establish a set of hubs throughout the state so that all residents of the state can access a hub via a local phone call. Local phone service is available between all pairs of adjacent counties in the state. Thus, if there is a hub in a given county, or in one of the adjacent counties, then residents of that county have the desired access.
County adjacencies are shown below. Values of 1 indicate counties that are adjacent to each other and values of 0 show counties that are not adjacent to each other. Each county is considered to be adjacent to itself.
|
County Adjacencies
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
|
1
|
1
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
2
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
3
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
4
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
|
5
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
|
6
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
|
7
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
|
8
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
|
9
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
0
|
|
10
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
|
11
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
|
12
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
|
13
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
|
14
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Popn
|
36,369
|
39,987
|
21,302
|
30,458
|
38,334
|
55,096
|
38,223
|
258,787
|
873,224
|
128,483
|
99,276
|
571,697
|
90,381
|
43,089
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Questions: Please use excel solver and also provide a "concise" algebraic formulation / narration)
a) Solve the Max Cover model for DixieNet with 1, 2 and 3 hubs.
b) DixieNet has decided to use sales representatives to generate sales at the grass roots level. Each sales rep will be assigned a primary county and a secondary county. The sales rep then travels within these 2 counties only. That way, once a sales rep is assigned a particular primary and secondary country, those populations are covered.
b) i) Assuming that you initially had 1 sales rep, which county would you assign him to (primary and secondary) in order to maximize population coverage? Develop a Greedy Heuristic for solving this.
b) ii) Suppose you had 2, 3, 4, or 5 sales reps. How would you assign them? Develop a Greedy Heuristic for solving this and also, the most concise Integer programming model to solve the problem optimally. Show the algebraic formulation and implement and solve it in excel.
|
What is the force exerted by charges a and b on c
: Two electrons repel each other with a force of 10-8N. How far apart are they?
|
|
What is the total force acting on each charge
: Three test charges, each with a charge of +1x10-6 C, are located at the points of an equilateral triangle. If the legs of the triangle are 10 cm long, what is the total force acting on each charge? (Assume vacuum, or dry air.)
|
|
Analysts worried that in pushing prices
: Coach Inc.'s profit and sales fell over the holidays, and Wall Street is concerned the retailer's plan to improve its performance by going upmarket may not work out. Analysts worried that in pushing prices higher Coach was allowing itself to be under..
|
|
Influence other drivers to operate more safely
: Statistics demonstrate that other vehicle drivers contribute most often (make the errors leading to an accident) when involved in an accident with a large truck. What can be done by trucking companies to influence other drivers to operate more sa..
|
|
Problem regarding the linear programming-max cover
: DixieNet is an Internet service provider for residential customers in a southern state. The company is small now but plans to expand. Its first major goal is to establish a set of hubs throughout the state so that all residents of the state can ac..
|
|
Calculate the electric potential (phi) at various points
: Consider a circular disk with radius R that has a uniformly distributed surface charge of Q.
|
|
Find the mass of the pulley
: The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly one-half the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of t..
|
|
Determine number of permanent and temp operators
: They want to limit claims error to 25 per day total, and the perm generate .5 errors/day and temp generate 1.4 error per day. The perm operators are paid $465/day and temp/$42/day. Need to determine the number of permanent and temp operators to hi..
|
|
Find the mass of the pulley
: The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly one-half the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of t..
|