2 - How the formulation should change if Frostburg Wires want to maximize its pr

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 1,116

Explanation / 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

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