Question

2. Another smaller company in the same business and city, which is not subject to the city regulation, to stay competitive is following suit by relocating its warehouse that supplies its five outlets. The outlets are located at points Pi(1.1), Pz (2,4), Ps (4,3), P4 5,1), Ps (6,5). The amount of product movement between the warehouse and each of the outlets is proportional to: wi = 4, w-= 2, w,-6,wa - 2, W5-6. Rectilinear movement is used in this problem as well (a) Determine a location for the new warehouse that minimizes the sum of the weighted distances. (This is the total cost.) (b) Suppose the new warehouse cannot be located within 2 rectilinear distance units of an existing outlet (i.e., di 2 2). Determine the optimum location of the new warehouse either by construction of contour lines (which is time-consuming!) or simply by visual assessment of some obvious potential points. (Well, about 6 of them, and it will be acceptable if you provide some explanations.) (c) For the particular point selected, determine the total cost. d) Determine the location of the new warehouse if instead of the restrictions in part (b) the following restrictions are applied: x's5 and y's2

Answer 1

6 P5 P2 Centroid P3 2 P1 P4 2 4 6 X-

yn weiqhed distantes om - rnt with hast dsfante we s have = 3-7 Thex pints ose And b infeyechon raddu

n	x-val	y-val	Distance
1	0.338	2.887	80.30137
2	2.662	2.113	53.29084
3	2.02	2.721	56.95829
4	2.98	1.279	58.61802
5	3.742	4.983	57.2433
6	2.258	2.017	57.03334
7	3.017	1.258	58.69639
8	5.983	2.742	59.01584
9	6	3	58.25901
10	4	5	56.71835

From the above table, the new co-ordinates are - (2.662,2.113)

Ans c:

From the table, the total cost for this new co-ordinates is 53.29 units

Ans d:

The nearest point from actual centroid to the lines with new constraints would be the new ware-house

In this case, the constraint lines are x <= 5 , and y <= 2. And the centroid is (3.9,3.1)

The nearest point within the limits is (3.9,2)