# Formulate the transportation problem and find the optimal solution

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M/s ABC & CO. is interested in developing an advertising campaign that will reach to the persons belonging to four different age groups. Advertising campaign can be conducted through media M1, M2, and M3.Â  The following table gives the estimated cost in paise per exposure for each age group according to the media employed.Â  In addition, maximum exposure levels possible in each of the media, namely, M1, M2, and M3 are 40, 30, and 20 mns., respectively.Â  Also, the minimum desired exposures within each age group, namely 16-20, 21-25, 26-35, and 36 and above, are 30,25, 15, and10Â  mns. The objective is to minimize the cost of obtaining the minimum exposure level in each age group. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (Apr 2002)

 Media Age Groups 16-21 21-25 26-35 36 and above M1 12 7 10 10 M2 10 9 12 10 M3 14 12 9 12

(i)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Formulate the above as a transportation problem, and find the optimal solution.

(ii)Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Solve this problem if the policy is to provide at least 4 million exposures through M1 in the 16-20 age group and at least 8 million exposures through M1 in the age group 21-25.

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