Question

Question 4. The UAE celebr ates national day with children wearing new dresses embroidered with national flags. 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 from stitching a pant and AED 80 from 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 a tailor approximately 1.2 hours to cut and 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 dresses. The tailor wants to determine the number of pants (x1) and shirts (x2) to produce in order to maximize his revenue. Assume that fractional values of shirts and pants are acceptable. The ratio between sewing the number or pants and sewing the number of shirts is 1 to 2. The demand for the shirt is no less than 15 and at most 80. Formulate a linear programming model for this problem

please help thank you

Answer 1

linear programming model for this problem

max Z=3x1+40x2

1.2 x1 +0.9 x2<100

1.2 x1+ 0.5x2> 80