. A manufacturer makes sails for recreation and competitive sail boats. A recre- ational sail takes...

    

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. A manufacturer makes sails for recreation and competitive sail boats. A recre- ational sail takes 2 hours to cut and 4 hours to sew, while the competitive sail takes 3h to cut and 10h to sew. There are 150h available for cutting and 380h available for sewing. a) Write a system of linear inequalities that describes the above situation when r is the number of recreational sails and y is the number of competitive sails. Briefly justify why each inequality is correct. b) Sketch the feasible region (blank graph is below) and find the corners. c) The company makes $100 in profit for each recreational sail and $200 in profit for each competition sail. Consider the line 100x + 200y = 4000 and notice that it has multiple (21, in fact) integral solutions (that is, the points have integer coordinates) inside the feasible region. What do the production levels corresponding to the integral solutions all have in common? 50 45 40 35 30 25 20 15 10 5 Y 10 20 30 40 50 60 70 80 →x 90 100 . A manufacturer makes sails for recreation and competitive sail boats. A recre- ational sail takes 2 hours to cut and 4 hours to sew, while the competitive sail takes 3h to cut and 10h to sew. There are 150h available for cutting and 380h available for sewing. a) Write a system of linear inequalities that describes the above situation when r is the number of recreational sails and y is the number of competitive sails. Briefly justify why each inequality is correct. b) Sketch the feasible region (blank graph is below) and find the corners. c) The company makes $100 in profit for each recreational sail and $200 in profit for each competition sail. Consider the line 100x + 200y = 4000 and notice that it has multiple (21, in fact) integral solutions (that is, the points have integer coordinates) inside the feasible region. What do the production levels corresponding to the integral solutions all have in common? 50 45 40 35 30 25 20 15 10 5 Y 10 20 30 40 50 60 70 80 →x 90 100