A company has three treatments that it can apply to three different types of clothesnamely denims, linens, and suitingyielding 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.

Formulation

Let

D₁= the number of bolts of denims with Treatment 1

D₂= the number of bolts of denims with Treatment 2

D₃= the number of bolts of denims with Treatment 3

.

.

.

S₃= the number of bolts of Suiting with Treatment 3

Max 4(DW + DI + DP) + 5(LW + LI + LP) + 8(SW + SI + SP)

s.t.

2D₁ + 3L₁ + 3S₁ 80

3D₂ + 2L₂ + 3S₂ 90

4D₃ + 4L₃ + 3S₃ 65

D₁, D₂, D₃, ..., S₃ 0

Please solve model