2 300 The cost per unit produced with overtime for each week is $100 more than that for regular time. The cost of storage is $50 per unit for each week. There is already an nventory of two widgets on hand currently, but the company does not want to retain any widgets in inventory after 3 weeks Management wants to know how many units should be produced in each week in rder to minimize costs Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table. (10 points) 4. Consider the following problem (10 points) Maximize Z=6x,+x+2x subject to 4x1-2x2-x≤3 2x,+-x3≤1 ≥0,x2≥0,x3≥0 Let x4, 5, and x6 denote the slack variables for the respective constraints. After you apply the simplex method, a portion of the final simplex tableau is as follow Basic variable Coefficient of XI X2 X3 X4 X5 Right side X3 2 0 Use the fundamental insight to identify the missing numbers in the final simplex tableau 5. Consider the following problem(20 points) Maximize Z=2x,+7x,-3x x1+3x2+4x3≤30 subject to x,+4x2-x,<10 x1≥0,x2≥0,x3≥0 The corresponding final set of equations yielding the optimal solution is2 1 2 3 2 2 1 2 1 2 300 500 400 The cost per unit produced with overtime for each week is $100 more than that for regular time. The cost of storage is $50 per unit for each week. There is already an inventory of two widgets on hand currently, but the company does not want to retain any widgets in inventory after 3 weeks. Management wants to know how many units should be produced in each week in order to minimize costs. Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table. (10 points) 4.Consider the following problem (10 points) ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ ≥ ≥ ≥ + + ≤ − − − ≤ + + ≤ = + + 0, 0, 0 1 2 1 2 3 2 3 4 2 2 2 1 2 2 6 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x x x x subject to Maximize Z x x x Let x4,x5, and x6 denote the slack variables for the respective constraints. After you apply the simplex method, a portion of the final simplex tableau is as follows: Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 2 0 2 X5 (1) 0 1 1 2 X3 (2) 0 -2 0 4 X1 (3) 0 1 0 -1 Use the fundamental insight to identify the missing numbers in the final simplex tableau. 5. Consider the following problem (20 points) ⎪ ⎩ ⎪ ⎨ ⎧ ≥ ≥ ≥ + − ≤ + + ≤ = + − 0, 0, 0 4 10 3 4 30 2 7 3 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x subject to Maximize Z x x x The corresponding final set of equations yielding the optimal solution is