Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a three-hour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible promotion options are playing free gigs, making a demo CD, hiring an agent, handing out fliers, and creating a Web site. Each free gig costs them $200 for travel and equipment but generates about three paying gigs. A high-quality studio demo CD should help the band book 20 gigs but will cost $1,000. A demo CD made on home recording equipment will cost $400 but may result in only ten bookings. A good agent will get the band 12 gigs but will charge $1,500. The band can create a Web site for $350 and would expect to generate six gigs from this exposure. They also estimate that they may book one gig for every 500 fliers they hand out, which would cost $0.08 each. They don't want to play more than seven free gigs or send out more than 2,500 fliers, and can only produce one high-quality demo CD, produce one home demo CD, hire one agent, and make one Web site. Develop and solve an integer optimization model to find the best promotion strategy to maximize their profit. Which combination of promotional options and quantities maximizes the profit within the constraints? (Type whole numbers.) Promotional Option Free gigs High-quality demo CD Homemade demo CD Agent Fliers Web site Number Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a three-hour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible promotion options are playing free gigs, making a demo CD, hiring an agent, handing out fliers, and creating a Web site. Each free gig costs them $200 for travel and equipment but generates about three paying gigs. A high-quality studio demo CD should help the band book 20 gigs but will cost $1,000. A demo CD made on home recording equipment will cost $400 but may result in only ten bookings. A good agent will get the band 12 gigs but will charge $1,500. The band can create a Web site for $350 and would expect to generate six gigs from this exposure. They also estimate that they may book one gig for every 500 fliers they hand out, which would cost $0.08 each. They don't want to play more than seven free gigs or send out more than 2,500 fliers, and can only produce one high-quality demo CD, produce one home demo CD, hire one agent, and make one Web site. Develop and solve an integer optimization model to find the best promotion strategy to maximize their profit. Which combination of promotional options and quantities maximizes the profit within the constraints? (Type whole numbers.) Promotional Option Free gigs High-quality demo CD Homemade demo CD Agent Fliers Web site Number
