Question

Save Score: 0 of 1 pt 5 of 7 (3 complete) MN Score: 28.57%, 2 of 7 4.2.21-BE Question Help 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 48 pounds of foam and 120 labor-hours a week. Us 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. V M (Simplify your answers.) Enter your answer in the edit fields and then click Check Answer Check Answe Clear All

Answer 1

Given that Let 'x' be the number of basket balls and 'y' be the number of footballs we get from the given data a linear programming problem maximize M = 2.5 x + 2 y subject to the constraints { 4x + 3y lessthanorequalto 48 times 16 20x + 30 y lessthanorequalto 120 times 60 x greaterthanorequalto 0 y greaterthanorequalto 0 Then we can write of this problem maximize M = 2.5x + 2 y subject to the constraints {4x + 3y lessthanorequalto 768 20x + 30 y lessthanorequalto 7200 x greaterthanorequalto 0 y greaterthanorequalto 0 The corresponding system to the linear equations with stack variables is \r\n {4x + 3y + u = 768 20x + 30 y + v = 7200 - 2.5 x - 2y + M = 0 we must find that solution of the system for which x greaterthanorequalto 0, y greaterthanorequalto 0, u greaterthanorequalto 0, y greaterthanorequalto 0 and 'M' is as latge as possible The initial simplex is [x 4 20 - 2.5 y 3 30 - 2 u 1 0 0 v 0 1 0 mu 0 0 1]768 7200 0] To determine the pivot element