A textile manufacturer owns two plants that produce a certain type of fabric. After spinning the fibre, the manufacturer grades the produced yarn into three classes: high, medium, and low-grade. The textile manufacturer has a contract with a garment producer for at least 12 units of high-grade, 8 units of medium-grade and 24 units of low-grade yarn per week. The two plants have different operating characteristics as detailed below. A) Denote with xA and xB the number of days per week that plants A and B, respectively, are operated for. Write a linear program for the problem of minimizing the number of days each of the plants is operated for. [5 marks] B) Find the optimal solution using the graphical method. [5 marks]