The Metropolitan Arts Council (MAC) wants to advertise its upcoming season of plays, concerts, and ballets. A television commercial that costs $25,000 will supposedly reach 53,000 potential arts customers. The breakdown of the audience is as follows:

A newspaper ad costs $7,000, and the newspaper claims that its ads will reach an audience of 30,000 potential arts customers, broken down as follows:

A radio ad costs $9,000, and it is estimated to reach an audience of 41,000 arts customers, with the following audience breakdown:

The arts council has established several marketing guidelines. It wants to reach at least 200,000 potential arts customers. It believes older people are more likely to buy tickets than younger people, so it wants to reach at least 1.5 times as many people over 35 as people under 35. The council also believes women are more likely to instigate ticket purchases to the arts than men, so it wants its advertising audience to be at least 60% female.
a. Formulate and solve an integer programming model for MAC to determine the number of ads of each type it should use at the minimum cost.
b. Solve this model without integer restrictions and compare theresults.

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Age Male Female e35 <35 2,000 7,000 20,000 14,000 Female 8,000 4,000 Male Age z35 35 12,000 6,000 Age Male Female 235 <35 7,000 10,000 11,000 13,000