2 - How the formulation should change if Frostburg Wires want to maximize its pr
ID: 3369671 • Letter: 2
Question
2 - How the formulation should change if Frostburg Wires want to maximize its profit? (note that profit = revenue - cost)
ostburg 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. Having this information answer the following questions.
Product Units Ordered W045C 1,400 W023C 250 W005X 1,510 W007X 1,116Explanation / Answer
let us produce a,b,c,d units of W045C, W023C, W005X and W007X respectively
total revenue
100a+80b+130c+175d
total cost
66a+50b+70c+150d
net profit
34a+30b+60c+25d
now we need to maximize
34a+30b+60c+25d
subject to
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