Question

The Tinyton Public School Board is taking bids on the city’s four school bus routes. Four companies have made bids. X denotes that a particular company did not make a bid on a particular route.

	Route 1	Route 2	Route 3	Route 4
Company 1	2500	3000	1500	X
Company 2	X	4000	X	4000
Company 3	3000	X	2000	X
Company 4	X	X	4000	5000

1. Assume the bidder can be assigned only one route. Minimize Tinyton’s cost of running the four bus routes. (10 points)
2. Assume the bidder can be assigned two routes. Minimize Tinyton’s cost of running the four bus routes. (10 points)

Answer 1

The above picture shows the final matrix after solving it. At first, select the cell with lowest cost in the table. It is shown by encircling with pencil and naming it as 1. Then cut the entire row and entire column of the cell. Next, again select the cell with the lowest cost in the table from the remaining uncut values. The second cell selected is shown by circle no. 2 . Then we carry out similar steps for the remaining routes. It should be noted that we need to select for route no. 2 before route no. 4 to assign values as viceversa will lead to no values left for route no.2. After completion, add all the selected values for the final answer which is 1500+3000+4000+5000= 13500

b)

The above picture shows the solution b. This assignment method is a little different from solution 'a' as one company can have two routes. So, in place of cutting out the entire row, cut only the entire column of the selected cell. Keep in mind that each row can have only two selected values. After assigning two values for one company do not select any more values from the same company's row. The final answer is the sum of the selected values that is 1500+2500+4000+4000=12000

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