Question

11. A local television station plans to drop four Friday evening programs at the end of the sea- son. Steve Botuchis, the station manager, developed a list of six potential replacement pro- grams. Estimates of the advertising revenue (in dollars) that can be expected for each of the new programs in the four vacated time slots are as follows. Mr. Botuchis asked you to find the assignment of programs to time slots that will maximize total advertising revenue. 5:00– 5:30 P.M. 5000 7500 8500 7000 7000 6000 5:30– 6:00 P.M. 3000 8000 5000 6000 8000 4000 Home Improvement World News NASCAR Live Wall Street Today Hollywood Briefings Ramundo & Son 7:00– 7:30 P.M. 6000 7000 6500 6500 3000 4500 8:00– 8:30 P.M. 4000 5500 8000 5000 6000 7000

PLEASE SHOW HOW YOU GOT THE ANSWERS BY HAND! NOT BY EXCEL!

Answer 1

Solution by Hungarian method is following:

Hungarian Method НІ WN NL WST HB RS 5-5:30 -5000 -7500 -8500 -7000 -7000 -6000 5:30-6 -3000 -8000 -5000 -6000 -8000 -4000 7-7:30 -6000 -7000 6500 -6500 -3000 -4500 8-8:30 -4000 -5500 -8000 -5000 -6000 -7000 Column reduction - Subtract the smallest element in each column from every element in that column 5-5:30 5:30-6 7-7:30 8-8:30 3500 5000 1000 4000 WN 10000 0 2500 NL 0 3000 5000 WST 1500 2000 500 3000 HB 15000 4000 2000 RS 2500 4000 2500 1000 Row reduction - Subtract the smallest element in each row from every element in that row 5-5:30 5:30-6 7-7:30 8-8:30 НІ 2500 40000 3000 WN 10000 0 2500 NL O 3000 5000 WST 1000 15000 2500 HB 15000 4000 2000 RS 1500 3000 15000

Now we test whether it is possible to make an assignment using only zero distances. (a) Starting with row 1 of the matrix, we examine rows one by one until a row containing exactly single zero elements are found. We make an experimental assignment to that cell. Then we cross all other zeros in the column in which the assignment was made. (b) When the set of rows has been completely examined an identical procedure is applied successively to columns. Starting with Column 1, we examine columns until a column containing exactly one remaining zero is found. We make an experimental assignment in that position and cross other zeros in the row in which the assignment was made. It is found that no additional assignments are possible. Thus, we have the complete Zero assignment HI 8-8:30 3000 2500 WN NL WST HB RS | 5-5:30 5:30-6 7-7:30 2500 40000 10000 0 0 3000 500 1000 15000 1500 4000 1500 3000 1500 2500 2000 0 10 Optimal assignment of programs to time slots Program TimeSlot Ad Rev НІ WN 7-7:30 7000 NL5 -5:30 8500 WST 0 HB 5:30- 6 8000 RS 8-8:30 7000 Total Ad Revenue 30500 Total ad revenue resulting from optimal assignment = 30,500