any widgets in inventory after 3 weeks Management wants to know how many units should be produced in each week order to minimize costs Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table. (10 points) Solution: The transportation tableau is Unit cost Supply 1(RT) 400 I(OT 400 450 500 2(RT) 500 550 2(OT) 600 650 3(RT) 3(OT) 500 Demand 4. Consider the following problem (10 points) Maximize z=6 )x1+x2+2 2x,+2 2 4x,-2 3 subject to x,+2x,+-x,≤1 x1≥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 follows Basic variable E z I X2 3 X4 X5 6 Right side 0 X5 100 Use the fundamental insight to identify the missing numbers in the final simplex tableau Solution the final table is Basic variable Coefficient of Right side 0 X3 (2) 000 4 03 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) Solution: The transportation tableau is Unit cost 1 2 3 Supply Storage 0 50 100 2 1(RT) 300 350 400 2 1(OT) 400 450 500 2 2(RT) — 500 550 2 2(OT) — 600 650 1 3(RT) — — 400 1 3(OT) — — 500 2 Demand 3 3 3 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. Solution: the final table is: Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 0 7 0 6 X5 (1) 0 0 4 0 7 X3 (2) 0 0 4 1 0 X1 (3) 0 1 0 0 1