MusicTech manufactures and sells a portable music device called an mTune (similar to an iPod). At beginning of month 1, the company has $100,000 and 15 employees. Each machine the company owns has the capacity to make up to 900 mTunes per month, and each worker can make up to 600 mTunes per month. The company cannot use more labor or machine capacity than is available in any given month. Also, the company wants to have a nonnegative cash balance at all points in time. The company’s costs are the following:
■ Holding cost of $2 each month per mTune in ending inventory
■ Cost in month 1 of buying machines ($3000 per machine)
■ Raw material cost of $6 per mTune
■ Monthly worker wage of $3500
■ Hiring cost of $4000 per worker
■ Firing cost of $5000 per worker
In the absence of advertising, the monthly demands in months 1 through 6 are forecasted to be 5000, 8000, 7000, 6000, 5000, and 5000. However, MusicTech can increase demand each month by advertising. Every $10 (up to a maximum of $50,000 per month) spent on advertising during a month increases demand for that month by one mTune. The devices are sold for $75 each. The sequence of events in any month is that the company buys machines (month 1 only), hires and fires workers, makes the mTunes, advertises, pays all costs for the month, and collects revenues for the month. Develop a model to maximize profit (total revenue minus total costs) earned during the next six months.