Engineering Optimization
focuses on a medium-sized enterprise operating in the textile industry, specifically in apparel manufacturing. The primary challenge identified in the manufacturing unit was the efficient utilization of resources. The study outlined constraints related to various resources, including threads, fabrics, human resources, overheads, stitching, cutting, and finishing time. Additionally, it examined the production requirements for five products, namely Polo T-shirts, round neck T-shirts, basic T-shirts, singlets, and v-neck T-shirts. The resources requirement for the products and their respective maximum held value are as shown in Table 1 and Table 2 respectively. The demand and profit of the products are tabulated in Table 3
Table 1. Resource allocation product-wise
Products (T- shirts and pants) Polo T- shirt Basic T- shirt Round Neck T- shirt Singlets V neck T- shirt
Fabrics Thread gms meters 315 215 200 105 195 142 180 105 50 190
Labor RM 11 S 6 4.5 7
Overhead RM 31 19 20 15.5 37
Cutting (hours) .03
Sewing (hours) .35 .15 .16 .09 .31
Finishing Time (hours) .03 .02 .03 .02 to'
0 .02 .04
Table 2.Resource utilization and maximum value held in stock
Resource utilized Maximum held value Fabric(gram) 3,71,25,000 Thread(meter) 2,56,21,830 Labor(RM) 10,01,000 Overheads(RM) 50,00,000 Cutting(HOURS) 5,775 Sewing(HOURS) 44,500 Finishing(HOURS) 6,200
Table 3. Demand and profit table Polo T-shirt Basic T-shirt Round neck T-shirt Singlets V neck T-shirt Demand 15000 24000 12000 26000 00011 Profit 4.5 3.8 3.5 3 6.5
(a)
Formulate the LP model for the above
(b) Convert the LP model in (a)into simplex algorithm by using slack/surplus/artificial variables
(c)
Recommend an optimal product mix that maximizes company profits through the application of the Linear Programming method using Excel (Solver) software. Provide SOLVER Answer Report, Sensitivity Report,and Excel Sheet of your analysis
(d)
The company has some extra funds and is trying to increase the company's profit by
propose and justify which constraint(s) the company should invest in to increase its profit.
