Question

Glow Corp. manufactures and assembles light fixtures. The fixtures consist of 4 components: a mounting panel, a cosmetic ring, receptacles for the light bulbs, and a glass globe. The receptacles must be purchased, but the other components could be produced in-house. Glow must produce 8,000 fixtures in the next month. The in-house production facilities are limited, so some of the components may have to be purchased, rather than made in-house. The costs (in dollars) of manufacturing and purchasing the components are as follows:

                        Manufacture Purchase

          Mounting Panel         6          8

          Cosmetic Ring         4          7

          Glass Globe           18         23

The time in hours required to make each component in each of 3 departments is as follows:

                                Department

                             A      B      C

                                         ______________________________

          Mounting Panel     .2    .1     0

          Cosmetic Ring     .3    0     .05

          Glass Globe         0    .1    .4

                                         ______________________________

    Total Department hrs.   2000   900   3000   

Formulate a linear programming problem to determine what to make and what to buy in order to minimize total cost.  

Answer 1

Let the no. of Mounting Panels manufactured by Mm, purchased be Mp

Let the no. of Cosmetic Rings manufactured by Cm, purchased be Cp

Let the no. of Glass Globes manufactured by Gm, purchased be Gp

Total cost = 6*Mm + 8*Mp + 4*Cm + 7*Cp +18*Gm + 23*Gp

We have to minimize this cost

Hence, we get the objective function as:

Minimize Total Cost C = 6*Mm + 8*Mp + 4*Cm + 7*Cp +18*Gm + 23*Gp

Subject to constraints:

Mm + Mp = 8000....................Constraint for no. of mounting panels required for 8000 fixtures

Cm + Cp = 8000....................Constraint for no. of Cosmetic Rings required for 8000 fixtures

Gm + Gp = 8000....................Constraint for no. of Glass Globes required for 8000 fixtures

0.2*Mm + 0.3*Cm + 0*Gm <= 2000......Constraint for the availability of Dept. A hours

0.1*Mm + 0*Cm + 0.1*Gm <= 900.........Constraint for the availability of Dept. B hours

0*Mm + 0.05*Cm + 0.4*Gm <= 3000......Constraint for the availability of Dept. C hours

Mm, Mp, Cm, Cp, Gm, Gp >= 0...............Non-negativity constraint since no. of parts manufactured or purchased cannot be negative

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