Question: Metropolitan Arts Council

The Metropolitan Arts Council of San Francisco is planning an advertising campaign to promote its upcoming season of plays, concerts, and ballet performances. Several media opportunities are under consideration. A local television commercial announcement costing $25,000 is expected to reach an estimated 53,000 potential arts customers consisting of 12,000 males and 20,000 females over the age of 35 and 7,000 males and 14,000 females under 35. A newspaper ad costs $7,000 and is expected to reach 30,000 potential arts customers consisting of 12,000 males and 8,000 females over the age of 35 and 6,000 males and 4,000 females under 35. Lastly, a local radio program ad costing $9,000 is expected to reach an audience of 41,000 potential arts customers consisting of 7,000 males and 11,000 females over 35 and 10,000 males and 13,000 females under 35 years of age.
The arts council has established several guidelines in its promotional strategy. The council wants to reach at least 200,000 potential arts customers at the least cost. The council believes people over the age of 35 are more likely to purchase tickets to these events and wants to reach at least one and a half times as many potential customers who are over 35 as those who are under that age. The council also believes that women are more likely to initiate ticket purchases to the arts than men and therefore wants its overall audience to be at least 60% female.

a. Formulate a linear programming model that can be used to determine the optimal media selection strategy that yields the minimum cost solution for the Metropolitan Arts Council.

b. Determine the optimal media selection strategy using the Management Scientist software, including the quantity of each media type selected and the total cost. Provide a narrative that explains the Management Scientist solution used.