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An event management company, ABC, is planning a two-hour show to present the art and culture to tourists visiting Hawaii. ABC is engaging local groups of artists to perform during the show. The performance by these groups will include the following forms of art to varying extent: singing, playing musical instruments, acting, and dancing. The degree to which these art forms are present in the performance of these groups of artists is as follows.

Artist Group A: Singing (40%), Musical Instruments (20%), Acting (30%), and Dancing (10%)

Artist Group B: Singing (30%), Musical Instruments (5%), Acting (15%), and Dancing (50%)

Artist Group C: Singing (20%), Musical Instruments (30%), Acting (10%), and Dancing (40%)

Artist Group D: Singing (10%), Musical Instruments (20%), Acting (40%), and Dancing (30%)

The price charged by each artist group to ABC per hour is as follows:

Artist Group A: $250

Artist Group B: $200

Artist Group C: $300

Artist Group D: $275

Assume that each artist group is willing to perform for any fraction of time during the show and the price they charge would vary in the same proportion. For example, if Artist Group A performed for 24 minutes, the cost for ABC would be $100.

Also assume that the degree to which various art forms are present in the performance of these groups of artists would stay the same regardless of the duration. That is, whether Artist Group A performs for 5 minutes or for an hour, their percentage of singing, musical instruments, acting and dancing will stay the same.

ABC wants to keep the following considerations while planning their two-hour show. Singing should be at least 20%, performance on musical instruments should be at least 5%, acting should be at least 15%, and dancing should be at least 10%. Each of the four artist groups must perform for at least 5% of the total time of the show and no artist group should perform for more than 50% of the total time of the show.

With the above considerations in mind, ABC must decide the time for which each artist group must perform in the two-hour show to minimize the total cost.

Set up the above problem as a linear programming model in Excel with identification of decision variables, expression for the objective function, and equations/inequalities for the constraints. Use Solver in Excel to find the optimal solution and interpret it.