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Problem 1 (20 points) An advertising agency is conducting a 10-day advertising campaign for a local department store. The agency has determined that the most effective campaign would possibly include placing ads in three media: newspaper, television and social media. A total of $8,000 has been made available for this campaign, and the agency would like to distribute this amount in $2.000 increments across the media in such a fashion that an advertising exposure index is maximized. Research that has been conducted by the agency estimates the exposure in each of the media to depend on the amount of money spent as shown in the following table. For example, if $6.000 is spent in newspaper ads and $2,000 in television ads with no ads in social media, the estimated advertising exposure index will be 108. $ spent in thousands 2 4 6 Media 0 8 1. Newspaper 0 27 49 65 67 2. Television 0 43 65 80 83 3. Social media 0 35 48 68 70 a) Formulate the problem by dynamic programming, defining stages, decision variables, states, state transformation and recursive relationship. Problem 4 (10 points) Paltry Properties has just acquired four rental homes. Paltry wishes to have the houses painted within the next week so that all can be available for the prime rental season. This means that each house will have to be painted by a different contractor. The following table shows the bids (hundreds of dollars) received from four contractors on the four houses. Painter j Painter Bid (ci) House i 1 2 3 4 1 25 13 36 18 2 29 14 50 22 3 22 16 32 24 4 31 18 25 Paltry wants to decide which bids to accept in order to paint all houses at minimum total cost. (a) Formulate an assignment problem to choose the optimal plan. (b) Solve by the Hungarian algorithm. Write the optimal bid for each house and the minimum total cost. 40