An electronics firm manufactures radio models A B and C whic

An electronics firm manufactures radio models A, B and C, which have profit contributions of 16, 30 and 50 respectively. Minimum production requirements are 20, 120 and 60 for the three models, respectively. A dozen units of Model A requires 3 hours for manufacturing of components, 4 for assembling, and 1 for packaging. The corresponding figures for a dozen units of Model B are 3.5, 5, and 1.5, and for Model C are 5, 8, and 3. During the forthcoming week the company has available 120 plant-hours for manufacturing components, 160 for assembly, and 48 for packaging. Formulate this production planning problem as a linear programming problem. And provide the AMPL code (.mod and .dat)

Problem 3. An electronics firm manufactures radio models A, B and C, which have profit roblem 3. An electronics firm manufactures radao models contributions of 16, 30 and 50 respectively. Minimum production requirements are 20, 120 and 60 for the three models, respectively. A dozen units of Model A requires 3 hours for manufacturing of components, 4 for assembling, and 1 for packaging. The corresponding figures for a dozen units of Model B are 3.5, 5, and 1.5, and for Model C are 5, 8, and 3. During the forthcoming week the company has available 120 plant-hours for manufacturing components, 160 for assembly, and 48 for packaging. Formulate this production planning problem as a linear programming problem.

Solution

LP model formulationL the data of the problem is summarised as follows:

Resource / model Total availability (hrs)

Constraints A B C Total Hours Available

production requirement (units) 20 120 60

manufacturing time per dozen 3 3.5 5 120

Assembling time ( per dozen) 4 5 8 160

Packaging time (per dozen) 1 1.5 3 48

Contribution per unit (Rs) 16 30 50

Decision variables let x1,x2,x3= units of model A, B and C produced per week respectively.

The LP model

Maximize (total profit ) Z= 16x₁+30x₂+50x₃

Subject to constraints

Minimum production requirment constraints

X1 >=20

X2 >=120

X3 >=60

Manufacturing time constraints

(3x₁/12 +3.5x₂/12+5x₃/12)=<120

Assembling time constraints

4x₁/12+5x₂/12+8x₃/12 =<160

Packaging time constraints

X₁/12+1.5x₂/12+3x₃/12=<48

And x₁, x₂,x₃ >= 0