A manufacturer has just received a project to produce three types of products: type I, II and III. There are three types of machines set up for this project: Machine 1,2 and 3. The available capacity on the machine 1 and 2 that might limit output is summarized in the following table: The number of machine hours required for each unit of the respective products is as follows: There are requirements from the production and sale department as follows: (1) According to forecast the sales potential for product 3 is 35 units per week. (2) The company plans to utilize all the available time of machine 2. The unit profit would be $150,$120, and $125, respectively, on products 1,2 , and 3 . The objective is to determine the production volume for each product to maximize profit. Formulate a linear programming model for this problem and find the optimal solution