The Social Health Group is a nonprofit organization that conducts health talks for the local public. The organization conducts these talks at two different venues: Iron Age Hall and Virtual Town Amphitheatre. For the upcoming year, seven talks will be held.

The question that the organization faces is how many times in total should each of these seven talks be scheduled. A financial analysis has estimated revenues for each time a talk is held, and the organization has set the minimum number of times each talk is to be conducted based on a survey on the current health issues and needs of the local community. These data are shown in the table below.

The Iron Age Hall is available for 172 talks during the year, whereas the Virtual Town Amphitheatre is available for 108 talks. Due to the available space of the venues, Talk No. 2 and No. 5 must be held at the Iron Age Hall and the other talks can be held at either venue. The organization wants to achieve revenues of at least $130,000 while minimizing its production costs.

a. Develop and solve a linear optimization model to determine the best way to schedule the talks.

b. Is it possible to achieve revenues of $500,000?

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Talk 1 2 3 4 5 6 7 Revenue $1,198 $1,627 $986 $2,005 $1,592 $2,207 $792 Cost $98 $169 $79 $195 $180 $455 $382 Minimum Num- ber of Times Held 35 18 27 31 29 89 25