A Company Has Three Treatments That It Can Apply Three

question 52

Essay

A company has three treatments that it can apply three different types of clothes namely denims, linens and suiting yielding the profit $4, $5, and $8 per bolt respectively. One bolt of denims requires 2 hours in Treatment 1, 3 hours in Treatment 2 and 4 hours in Treatment 3. Similarly one bolt of linens requires 3 hours in Treatment 1, 2 hours in Treatment 2 and 4 hours in Treatment 3 while one bolt suiting requires 2 hours in Treatment 1, 3 hours in Treatment 2 and 4 hours in Treatment 3. In a week, total run time of each department is 80 hours, 90 hours, and 65 hours for Treatment 1, Treatment 2 and Treatment 3 respectively.
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Formulation
Let
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D₁ number of bolts of denims with Treatment 1
D₂ number of bolts of denims with Treatment 2
D₃ number of bolts of denims with Treatment 3
.
.
.
S₃ number of bolts of Suiting with Treatment 3
Max $4(DW + DI + DP) + $5(LW + LI + LP) +$8(SW + SI + SP)
s.t.
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2D₁ + 3L₁ + 3S₁ ≤ 80
3D₂ + 2L₂ + 3S₂ ≤ 90
4D₃ + 4L₃ + 3S₃ ≤ 65
D₁, D₂, D₃, …, S₃ ≥ 0