2. A jewelry manufacturer wants to optimally producing four different bracelets with their quantities denoted by...

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2. A jewelry manufacturer wants to optimally producing four different bracelets with their quantities denoted by x, x2, X3 and x4. The production of these bracelets require different amounts of gold, silver and time. A linear programming model has been formulated for determining the optimal quantities of the four different bracelets such that the total profit is maximized and the model is as follow: Max $900x, + $1250 x2 + 450x3 + $650x4 subject to 0.10x1 + 0.25x2 + 0.08x3 + 0.21x4 < 72 units (Gold) 3x1 + 3x2 + x3 + X4 < 1200 units (Silver) 3.6x1 + 4.8x2 + 2.5x3 + 3.5x4 < 2500 hours (Manufacturing Time) X1 + x2 < 500 (Limit on Total Quantity of Bracelets 1 & 2 Produced) X3 + x4 < 500 (Limit on Total Quantity of Bracelets 3 & 4 Produced) X1, X2, X3, X4 > 0 a. Determine the optimal solution to this linear programming model by Excel Solver. b. For each coefficient in the objective function, identify its range of change that the current optimal solution remains unchanged. c. For each of the first three constraints, identify the range of change of its right-hand-side value, in which the constraint's shadow price remains valid. d. One of the four bracelets is not produced in the optimal solution. How much would the objective coefficient of this bracelet be adjusted so that it is worthwhile to be produced? 2. A jewelry manufacturer wants to optimally producing four different bracelets with their quantities denoted by x, x2, X3 and x4. The production of these bracelets require different amounts of gold, silver and time. A linear programming model has been formulated for determining the optimal quantities of the four different bracelets such that the total profit is maximized and the model is as follow: Max $900x, + $1250 x2 + 450x3 + $650x4 subject to 0.10x1 + 0.25x2 + 0.08x3 + 0.21x4 < 72 units (Gold) 3x1 + 3x2 + x3 + X4 < 1200 units (Silver) 3.6x1 + 4.8x2 + 2.5x3 + 3.5x4 < 2500 hours (Manufacturing Time) X1 + x2 < 500 (Limit on Total Quantity of Bracelets 1 & 2 Produced) X3 + x4 < 500 (Limit on Total Quantity of Bracelets 3 & 4 Produced) X1, X2, X3, X4 > 0 a. Determine the optimal solution to this linear programming model by Excel Solver. b. For each coefficient in the objective function, identify its range of change that the current optimal solution remains unchanged. c. For each of the first three constraints, identify the range of change of its right-hand-side value, in which the constraint's shadow price remains valid. d. One of the four bracelets is not produced in the optimal solution. How much would the objective coefficient of this bracelet be adjusted so that it is worthwhile to be produced?

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