MS electronics supply highly complex components for military communications systems. Four products, named the MX range, share the labor hours available for each of the four production processes: wiring, drilling, assembly and finishing. For each product and each process, the hours of labor required for each unit of production and the total hours available per month are shown in the table below. The table also shows the profit earned per unit for each product and the minimum monthly demand for that product. Product Hours of labour per production unit Profit Minimum per unit (type of component) Wiring Drilling Assembly Finishing Demand Time Time Time Time (no. of units) MX1 05 15000 MX2 0.9 500 MX3 0.5 1800 MX4 2.5 2.0 0.6 900 Labor available 16000 18000 12000 10000 (hours per month) MS electronics need to know how many of each type of component they should produce each month to achieve their objective subject to unit profit figures and constraints mentioned above. This problem was formulated as a linear programming model and then solved using Microsoft's Excel Solver Add-in. The relevant Solver output is given in the Appendix. Using the Solver output and where necessary the information given above, answer the following questions. APPENDIX (please note Dem: Demand and 1E+30 = Infinity (no limit)) Objective Cell (Max) Cell Name Original Value Final Value $F$3 Objective 429940 On Variable Cells Cell Name $B$2 MX1 $C$2 MX2 $D$2 MX3 $E$2 MX4 Original Value 0 0 0 0 Final Value 15884 500 2136 900 Integer Contin Contin Contin Contin Slack 336 0 Constraints Cell $F$10 $F$11 $F$12 $F$5 $F$6 $F$7 $F$8 $F$9 Name Dem (MX2) Dem (MX3) Dem (MX4) Wiring Drilling Assembly Finishing Dem (MX1) Cell Value 500 2136 900 16000 15484.4 8862.8 10000 15884 Formula $F$10>=$H$10 $F$11>=$H$11 $F$12>=$H$12 $F$5=$H$9 Status Binding Not Binding Binding Binding Not Binding Not Binding Binding Not Binding 2515.6 3137.2 0 884 Variable Cells Cell $B$2 $C$2 $D$2 $E$2 Constraints Final Reduced Name Value Cost MX1158840 MX2 5000 MX3 2136 0 MX4 900 0 Objective Allowable Coefficient Increase 20 15 309.6 3 5 85 25 1.4 Allowable Decrease 1.35 1E+30 8.75 1E+30 R Cell $F$10 $F$11 $F$12 $F$5 $F$6 $F$7 $F$8 $F$9 Name Dem (MX2) Dem (MX3) Dem (MX4) Wiring Drilling Assembly Finishing Dem (MX1) Final Value 500 2136 900 16000 15484 8863 10000 15884 Shadow Price -9.6 0 -1.4 6 0 0 34 0 Constraint .H. Side 500 1800 900 16000 18000 12000 1 0000 15000 Allowable Increase 566.7 336 850 2210 1E+30 1E+30 840 884 Allowable Decrease 500 1E+30 900 840 2515.6 3137.2 368.3 1E+30 10 MS electronics think that a change in manufacturing location could increase profits by reducing costs. The following scenario is thought to be possible: the only change is that the unit profit for the MX4 increases by 10%. How would this change impact the optimal solution? The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. Nothing. The values of the decision variables, the shadow (dual) prices, and the objective function value will all remain the same. This change is not allowed. The problem will need to be resolved to find the new optimal solution. Objective function value will increase by 10%. The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same