(a) Kim Fashion factory manufactured adult and children shirts for selling to the fashion

stores in a town: man's shirt, woman's shirt, girl's shirt, and boy's shirt. The revenues are

$60, $50, $40, and $35 per shirt, respectively. The cost and meter of fabric required for each

shirt are shown as follows:

Man shirt Women shirt Girl shirt Boy shirt

Cost($) 30 25 18 15

Meter 3 4 2 2

There are 78,000 minutes of manufacturing time available. A man's shirt needs 5 hours to

manufacture, a woman's shirt needs 6 hours to manufacture, a girl's shirt needs 4 hours to

manufacture, and a boy's shirt needs 4 hours to manufacture. The total production of adult and

children shirts must be at least 290 units. The availability of fabric are 1000 meters. Also, the

production of the adult's shirt should be at least 40% of the children's shirt. The sensitivity

report of this problem is given in Figure 1 where the decision variables are defined as:

x1 = number of man's shirt manufactured

x2 = number of woman's shirt manufactured

x3 = number of girl's shirt manufactured

x4 = number of boy's shirt manufactured

Figure 1: Sensitivity analysis report

Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$4 X1 140 0 30 1E+30 $C$4 2.5 X2 0 -13 25 13 $D$4 1E+30 X3 150 0 22 2 $E$4 2 X4 0 -2 20 2 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $L$3 Manufacturing Time Constraint 1300 8 1300 150 $L$4 Fabric constraint 57.14 720 0 1000 1E+30 280 $L$5 Production Constraint 290 -10 290 13.33 30 $L$6 Ratio Constraint 80 0 0 80 1E+30