SMPO is a company that produces two types of metal containers for businesses. Type-A is the standard version; Type-B is a special version. Containers are manufactured through three major processes: process-1, process-2, and process-3. In process-1, a large machine is used to cut standard metal sheets into appropriate sizes. In process-2, another device bends the metal into shape. Process-3 involves joining the parts with a combination of soldering and riveting. SMPO's process-1 and process-2 are used for both types of containers. Separate process-3 departments are used for the final stage of production.

The production of one Type-A approximately requires 0.27 hours and 0.34 hours on the process-1 and process-2 machines, respectively. Similarly, the output of one Type-B requires 0.5 hours and 0.48 hours on the process-1 and process-2 machines, respectively. Both the process-1 and process-2 machines can operate for 750 hours each month. The Type-A process-3 department has a monthly capacity of 1,500 units. The Type-B process-3 department has a monthly capacity of only 1,350 units. Currently, SMPO is producing and selling 350 units of Type-A and 1,300 units of Type-B per month.

Type-A containers are sold for $1,790, and Type-B containers are sold for $1,995. SMPO's operation is relatively small in the industry, and management believes it cannot increase prices beyond these levels because of the competition. However, the marketing department believes that SMPO can sell as much as it can produce at these prices.

(a) Formulate a linear programming model for this problem. [8 marks]

(b) Which of the constraints for the models formulated in part (a) are binding or nonbinding at the optimal solution? Show your calculations and compare your results with those in the Answer report. [4 marks]

(c) Is the optimal solution to this problem formulated in part (a) unique, or are there alternate optimal solutions? Justify your answer. [3 marks]