dolution

A company produces two types of products: product A and product B with respective profits of $7 and S4. The company would like to achieve $108 in profits. A total of 72 labor hours are available for production with possible overtime. One unit of product A requires 5 hours, while one unit of B requires 3 hours. The company aims to satisfy the market demand, which requires at least 9 units of product A be produced and at least 13 units of Product B be produced. Suppose that the company incurs a $3 penalty for each dollar below the profit target. Moreover, a $6 penalty is incurred for each hour of overtime used, and a S3 penalty is incurred for each hour of unused labor. Additionally, a penalty of $10 is incurred for each unit (A or B) of unmet demand. Formulate the problem using goal programming.