Business Studies, asked by jonathanwestermen, 2 months ago

I'm stuck at this question

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Answered by harshmed4u

Answer:

Solution: This problem could be solved using the transportation technique.

However, only five of the routes will be used and so an additional four

routes would have to be included at zero level in order to determine

shadow costs and thus test for optimality.

The problem is to select five elements from the matrix of Table 1 such that

there is one element in each row, one in each column, and the sum is the

minimum possible.

Step 1. Subtract the smallest element in each row from every

element in that row. This yields the following new matrix of distances:

Table 2

Step 2. Subtract the smallest element in each column of Table 2

from every element in that column. This yields the following distance

matrix:

Table 3

Step 3. Test whether it is possible to make an assignment using

only zero distances. If this is possible, clearly the assignment must be an

optimal one, since no element in the matrix of Table 3 is negative. It can

be shown that a "zero assignment" can only be made if the minimum

number of horizontal and vertical lines necessary to cover all zeros in the

matrix equals the number of rows in the matrix– –5 in this case. Applying

this test to the matrix of Table 3, we find that three lines, suitably chosen,

cover all zeros (see Table 4).

Thus a zero assignment is not possible at this stage.

Step 4.

(i) Find the smallest uncovered element as a result of Step 3. Call

this element x.

(ii) Subtract x from every element in the matrix.

(iii) Re-add x to every element in all rows and columns covered by

lines.

(iv) Re-apply the test of Step 3 to the resulting matrix. The effect of

(ii) and (iii) above is to:

Subtract x from all uncovered elements, add x to elements at the

intersection of two lines, and leave unchanged elements covered by one

line.

Applying Step 4 to the matrix of Table 3 it is noted that x = 15, and the

new matrix is given in Table 5.

The zeros in this matrix cannot be covered by fewer than five lines and

hence a zero assignment is now possible. This is indicated below:

Table 6

To reach this assignment proceed as follows:

Columns 1 and 3 each contain only one zero. These zeros must,

therefore, form part of the optimal assignment and are indicated in bold

type. The additional zeros in rows 2 and 4 can now be crossed out as they

cannot feature in the final assignment. This leaves column 4 with one zero

remaining. This is indicated in bold type, the two other zeros in row 5 are

crossed out. Column 5 now has one zero remaining and, when this is

eliminated, the zero at the intersection of row 3 and column 2 completes

the assignment.

The minimum assignment is therefore:

Route

Distance

200 miles

130

110

Total distance travelled: 570 miles.

Explanation:

ok so here is ur answer

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