3. Note the limited production capacity in each plant, given below. For example, Plant 1 cannot produce more than 1200 units. Which constraints describe this situation? a. Plant 1 <= 1200; Plant2 <= 900; Plant3 <= 850 b. X11+X12+X13<= 1200; X21+X22+X23 <= 900; X31+X32+X33 <= 850 c. X11+X21+X31 <= 1200; X12+X22+X32 <=900; X31+X32+X33 <= 850 d. None of the above. 4. To prevent layoffs management wants the percent of the available capacity used for production be equal among all plants (for example, capacity in plant 1 is 1200 units. If this plant produces 500 units, it uses < 500/1200 = 41.67% of its capacity. Then all the plants must use 41.67% of their capacity that is, equal workload for all plants). Write the constraints needed to secure this requirement (in the Answer sheet). Plant2 Plant3 Plant1 1200 units Capacity avail 900 850 Storage avail 13000 sqft 12000 5000 Required starage per unit 20 sq-ft 15 12 Large Medium Small Profit/unit $1000 1100 700
Variable Cells Constraints Cell $T$25 $U$25 $V$25 $T$26 $U$26 $V$26 $T$27 $U$27 $V$27 Cell Final Name Value Large Plant 346.0784 Large Plant 0 Large Plant 0 Medium Pl 242.1569 Medium Pl: 441.1765 Medium Pl: 416.6667 Small Plant 0 Small Plant 0 Small Plant 0 Final Name Value Production 588.2353 Production 441.1765 Production 416.6667 Equal % Pla 0.490196 Equal % Pla 0.490196 Space Occu 11764.71 Space Occu 6617.647 Space Occu 5000 Large Prod 346.0784 Medium Pr 1100 Small Prod 0 Large Prod 346.0784 1100 0 $T$28 $U$28 $V$28 $T$32 $U$32 $T$37 $U$37 $V$37 $W$25 $W$26 $W$27 $W$25 $W$26 Medium Pr $W$27 Small Prod Reduced Cost Shadow Price oooo 0 0 0 -300 -300 -300 oooggom 0 0 1200000 2100000 289.2156863 0 100 0 0 0 0 0 0 Objective Coefficient 1000 1000 1000 1100 1100 1100 700 700 700 Constraint R.H. Side 1200 900 850 0 0 13000 12000 5000 1000 1100 700 900 1200 750 Allowable Decrease 0 1E+30 1E+30 100 0 0 1E+30 1E+30 1E+30 Allowable Decrease 1E+30 611.7647 1E+30 458.8235 1E+30 433.3333 0.051470588 0.288399 0.051470588 0.164799 1E+30 1235.294 1E+30 5382.353 525 1196.61 1E+30 653.9216 100 242.1569 1E+30 700 1E+30 553.9216 1E+30 100 1E+30 750 Allowable Increase Allowable Increase 100 0 0 0 1E+30 1E+30 300 300 300
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