Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$10 Xa1 0 1 14 1E+30 1 $C$10 Xa2 70 0 9 0 12 $D$10 Xa3 0 9 16 1E+30 9 $E$10 Xa4 80 18 1 0 $B$11 XB1 50 11 1 0 $C$11 XB2 0 1 8 1E+30 1 $D$11 XB3 0 2 7 1E+30 2 $E$11 Xb4 160 0 16 0 1 $B$12 Xc1 80 0 16 0 2 $C$12 Xc2 0 0 12 1E+30 0 $D$12 Xc3 180 0 10 2 10 $E$12 Xc4 0 1 22 1E+30 1 OO Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$13 1 130 16 130 60 80 $C$13 2 70 12 70 50 70 $D$133 180 10 180 60 180 $E$13 4 240 21 240 50 80 $F$10 A 150 -3 150 80 50 $F$11 B 210 -5 210 80 50 $F$12C 260 0 320 1E+30 60 nswer the following questions. a) (4 points) What is the current optimal solution? Calculate the optimal cost. b) (7 points) For which values of the per ton shipment cost from Birmingham to Detroit current optimal solution remains optimal? c) (7 points) The mill in Birmingham has the option to work overtime and can produce up to 60 more tons. Working overload will cause a weekly cost of $250 in addition to regular production costs. Would you use the overtime option? d) (7 points) A steel supplier in Detroit offers to provide 60 tons of steel for a price which would increase total cost by $1000 (in addition to production cost of plants of the firm). Would you accept the deal? Question 4: (25 pts) Steel mills in three cities produce the following amounts of steel: Location Weekly Production (tons) A. Bethlehem 150 B. Birmingham 210 C. Gary 320 680 These mills supply steel to four cities, where manufacturing plants have the following demand: Weekly Demand (tons) 130 Location 1. Detroit 2. St. Louis 3. Chicago 4. Norfolk 70 180 240 620 Shipping costs per ton of steel are as follows: To (cost) 2 3 1 From A B $14 11 16 $ 9 8 12 $16 7 10 $18 16 22 Because of a truckers' strike, shipments are prohibited from Birmingham to Chicago. Formulate this problem as a linear programming model and solve it by using the computer. The problem is modelled below and solved (therefore, you will not model the problem) and the following sensitivity analysis report is the output. Min 14X21+9X 2+16X 3+18X4+11Xb1+8%b2+7X03+16%b4+16Xc1+12X_2+10Xc3+22Xca s.t. Xo1+X 2+X 3+X24 S 150 X. 3+Xo3+Xc3 2 180 Xb1+Xb2+Xo3+Xb4 210 X 4+Xb4+Xc4 2 240 Xc1+Xc2+Xc3+Xca s 320 Xb3 = 0 Xa1+Xuu+Xc1 2 130 All Xij 20 Xa2+X+2+Xc2270