Find the best promotion strategy to maximize their profit.

Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a 3-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 as follows:

• playing free gigs

• making a demo CD

• hiring an agent

• handing out fliers

• creating a Web site

Each free gig costs them about $250 for travel and equipment but generates about three paying gigs.

A high-quality studio demo CD should help the band book about 20 gigs but will cost about $1,000. A demo CD made on home recording equipment will cost only 400 but may result in only 10 bookings. A good agent will get the band about 15 gigs but will charge 1,500. The band can create a Web site for400 and would expect to generate 6 gigs from this exposure. They also estimate that they may book 1 gig for every 500 fliers they hand out, which would cost0.08 each. They don’t want to play more than 10 free gigs or send out more than 2,500 fliers. Develop and solve an integer optimization model to find the best promotion strategy to maximize their profit.