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F1: # of cartons of face cream to be produced in 1st shift F2: # of cartons of face cream to be produced in 2nd shift B1: # of cartons of Body cream to be produced in 1st shift

B2: # of cartons of Body cream to be produced in 2nd shift H1: # of cartons of Hand cream to be produced in 1st shift H2: # of cartons of Hand cream to be produced in 2nd shift

Fs: # of cartons of Face cream to be subcontracted to local vendor Bs: # of cartons of Face cream to be subcontracted to local vendor

The goal is to minimize the total production and subcontracting cost the products while meeting demand, labour, and raw mterial constraints

Decision Variable F1 B1 H1 F2 B2 H2 Fs Bs Available Cost

1st shift Labor Stage 1st 1.5 1.8 1 0 0 0 0 15000 $8.50

Labor Stage 1st 0.8 1 0.5 0 0 0 0 0 10000 $9.25

2nd Shift Labor Stage 1st 0 0 0 1.5 1.8 1 0 0 13500 $9.35

Labor Stage 1st 0 0 0 0.8 1 0.5 0 0 9000 $10.18

Raw Mat A A 5 8 3 5 8 3 0 0 200000 $1.00

Raw Mat B B 7 4 9 7 4 9 0 0 150000 $1.50

Cost ($ 35.65)($ 38.55) ($ 29.63) ($ 37.67) ($ 41.01) ($ 30.94) ($ 40.00) ($ 55.00) $1,066,563.75 Total Cost

Optimal Production Qty -0.00000099999998333750.0000028249.999998 0 0 6750.000002 10000 1249.999998

Demand Constraint for Face cream

-0.0000009999999833 0 10000 10000 = ( 10,000) Demand Constraint for body

cream 3750.000002 0 1249.999998 5000 = ( 5,000)

Demand Constraint for hand cream

8249.999998 6750.000002 15000 = ( 15,000) Available labour hrs for stage 1

in 1st shift 1.5 1.8 1 0 0 0 0 0 15000 <= ( 15,000)

Available labour hrs for stage 2 in 1st shift

0.8 1 0.5 0 0 0 0 0 7875 <= ( 10,000) Available labour hrs for stage 1

in 2nd shift 0 0 0 1.5 1.8 1 0 0 6750.000002 <= ( 13,500)

Available labour hrs for stage 2 in 2nd shift

0 0 0 0.8 1 0.5 0 0 3375.000001 <= ( 9,000)

Raw Mat avail for A 5 8 3 5 8 3 0 0 75000.00001 <= ( 200,000)

Raw Mat avail for B 7 4 9 7 4 9 0 0 150000 <= ( 150,000)

1- Production Schedule: F1 F2 B1 B2 H1 H2 Fs Bs

0 3750.0000028249.999998 0 0 6750.000002 10000 1249.999998

2- Based on the above results, 10,000 cartons of face cream and 1250 cartons of body cream should be subcontracted

3- Objective function value = $1,066,546.88

4- Labor hours of Stage 1 in shift 1 are completely utilized. Raw material B is also completely consumed.

B1: # of cartons of Body cream to be produced in 1st shift

H2: # of cartons of Hand cream to be produced in 2nd shift