1 - Formulate a LP problem for Frostburg Wires to maximize its revenue . Clearly

Question

1 - Formulate a LP problem for Frostburg Wires to maximize its revenue. Clearly state your decision variables, objective function and constraints.

Wires produces four types of wires shown as W045C, W023C, W005X and W007X. To produce wire, 4 manufacturing stages, namely drawing, extrusion, winding and packaging is required. April orders for Frostburg Wires is as follows:

The cost of producing one unit of each product as well as its selling price is as follows:

Each product unit needs a certain amount of time (in hours) at each production stage as follows:

Plant capacity for each stage of production in terms of hours available is as follows:

Assume that Frostburg Wires can fulfill an order fully or partially.

Product Units Ordered W045C 1,400 W023C 250 W005X 1,510 W007X 1,116

Explanation / Answer

Answer

Formulation of LP Model for frostburg wire to maximise:-

Consideration-

Let us Produce a,b,c,d units of W045C, W023C, W005X and W007X respectively as shown above

Here, Total revenue

100a+80b+130c+175d

Total cost is equal to ;

66a+50b+70c+150d

Therefore ,Net profit

34a+30b+60c+25d

Now ; we need to maximize

34a+30b+60c+25d

Subject to Constraint

1a+2b+0c+d <= 4000

1a+ 1b+ 4c + 1d<=4200

1a+ 3b+ 0c+ 0d<=2000

1a + 0b+ 3c + 2d <=2300

if we assume order can be partial then we dont need the contraints on a,b,c,d

Product Material ($) Labor ($) Overhead ($) Selling Price ($) total cost ($) profit W045C 33 9.9 23.1 100 66 34 W023C 25 7.5 17.5 80 50 30 W005X 35 10.5 24.5 130 70 60 W007X 75 11.25 63.75 175 150 25

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