162 IHW6 OM338 SCModOpt F17 (1).pdf (page 1 of 3) Q Search When answering the questions in this homework, follow the guidelines for managerial problem definition and mathematical problem formulation in the document "Modeling Guidelines" Problem 1: AudioTech manufactures and sells a portable music device, and wants to plan production for the next six months. Manufacturing the device requires capacity on a specialized machine as well as labor. AudioTech needs to purchase the machines that it nceds at the beginning of Month 1 Each machine costs $ 3,000 and can manufacture up to 900 units of product per month. The monthly working time of each worker is enough to meet the labor requirement for month. units per : The raw material cost per unit of product is S6, and its selling price is $75. The company can purchase as much raw material as it needs each month. Holding finished products in inventory from one month to the next costs $2 per unit of ending inventory. The monthly worker wage is 3,500. At the beginning of Month 1, the company has 15 employees. Workers can be hired or laid off at the beginning of each month. The cost of hiring a worker is $4,000 and cost of laying off a worker is $5,000. In the absence of advertising, the monthly demands in months 1 through 6 are forecasted to be 5,000, 8,000,7,000, 6,000, 5,000, and 5,000. The company need not fully meet this demand, but cannot sell more than demand. AudioTech has the option to advertise each month to increase demand. Every $10 spent on advertising during a month increases demand for that demand by one unit in that month. Company policy specifies that no more than $50,000 must be spent on advertising in any month. The sequence of evints in any month is as follows: The company buys machines (in Month 1 only), hires or lays off workers, advertises, makes the product, collects the sales revenues for that month, and pays all costs for the month (including holding cost of ending inventory in that month, worker pay, advertising cost, etc.). At the beginning of Month 1, the company has $100,000 in cash. The company wants to maximize the total net profit (net of the cost of purchasing the machines and other expenses) over the next 6 months, but requires that the cash balance must never be negative in any month. The company does not have any product in inventory at the start of Month I. (a) Provide a managerial problem statement 162 IHW6 OM338 SCModOpt F17 (1).pdf (page 1 of 3) Q Search When answering the questions in this homework, follow the guidelines for managerial problem definition and mathematical problem formulation in the document "Modeling Guidelines" Problem 1: AudioTech manufactures and sells a portable music device, and wants to plan production for the next six months. Manufacturing the device requires capacity on a specialized machine as well as labor. AudioTech needs to purchase the machines that it nceds at the beginning of Month 1 Each machine costs $ 3,000 and can manufacture up to 900 units of product per month. The monthly working time of each worker is enough to meet the labor requirement for month. units per : The raw material cost per unit of product is S6, and its selling price is $75. The company can purchase as much raw material as it needs each month. Holding finished products in inventory from one month to the next costs $2 per unit of ending inventory. The monthly worker wage is 3,500. At the beginning of Month 1, the company has 15 employees. Workers can be hired or laid off at the beginning of each month. The cost of hiring a worker is $4,000 and cost of laying off a worker is $5,000. In the absence of advertising, the monthly demands in months 1 through 6 are forecasted to be 5,000, 8,000,7,000, 6,000, 5,000, and 5,000. The company need not fully meet this demand, but cannot sell more than demand. AudioTech has the option to advertise each month to increase demand. Every $10 spent on advertising during a month increases demand for that demand by one unit in that month. Company policy specifies that no more than $50,000 must be spent on advertising in any month. The sequence of evints in any month is as follows: The company buys machines (in Month 1 only), hires or lays off workers, advertises, makes the product, collects the sales revenues for that month, and pays all costs for the month (including holding cost of ending inventory in that month, worker pay, advertising cost, etc.). At the beginning of Month 1, the company has $100,000 in cash. The company wants to maximize the total net profit (net of the cost of purchasing the machines and other expenses) over the next 6 months, but requires that the cash balance must never be negative in any month. The company does not have any product in inventory at the start of Month I. (a) Provide a managerial problem statement