A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor and brings a profit of $2.50. The football uses 3 ounces of foam and 30 minutes of labor and brings a profit of $2. The manufacturer has available 51 pounds of foam and 124 labor-hours a week. Use the simplex method to determine the optimal production schedule so as to maximize profits. Show that the geometric method gives the same solution. Set up the initial simplex tableau. Let x and y be the number of basketballs and footballs that are produced each week, respectively. y u V u 4 3 1 816 20 30 1 0 7440 V M - 2.5 -2 1 (Simplify your answers.) The maximum profit is $ 538 . This occurs when the manufacturer makes 36 basketball and 224 footballs each week. (Simplify your answers.) To show that the geometric method gives the same solution, identify the vertices of the graph of the feasible set. Let x and y be the number of basketballs and footballs that are produced each week, respectively. (0,0),(0,248),(36,244).(204,0) (Type an ordered pair. Use a comma to separate answers as needed.)

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