On the UAE national day, children wear new clothes with the national flag embroidered on them. A tailor has three weeks before the national day and plans to work for up to 40 hours per week for the next three weeks. He earns a revenue of AED100 for stitching a pant and AED 80 for stitching a shirt. He has a stock of 90 meters of cloth and 80 units of packaging material. A pant requires 0.8 meters of cloth and a shirt, 0.9 meters of cloth. It takes the tailor approximately 1.2 hours to stitch a pant and 0.9 hours to stitch a shirt. After stitching, the pants and shirts are packaged separately using special packaging material. A pant needs 1.2 units of packaging material whereas a shirt needs 0.5 units of packaging material. He has enough demand for both. The tailor wants to determine the number of pants (x1) and shirts (x2) he needs to produce in order to maximize his revenue. Assume that fractional values of shirts and pants are acceptable.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.