LINEAR PROGRAMMING

PARTA: Sadella Sdn. Bhd. is a factory which manufactures working suits, abayas and kurungs for Lazara Stores. Lazara will aconpt all the production supplied by Sadella. The production process includes cutting, sewing and packaging. The maximum available daily time for each cloth to go through each stage of production (cutting, sewing and packaging) are 280 minutes, 240 minutes and 350 minutes, respectively. Table 1 gives the time requirements (in minutes) and profit per unit for the three products: Table 1 Minutes per unit Unit Profit CRM) Products Cutting Sewing Packaging 30 20 10 Suits 10 20 Bag 30 Abayas 20 10 30 Kurungs Let *; - number of suits produced daily, *z number of abayas produced daily. *; - number of kurungs produced daily. After formulating the LP model to determine the maximum profit, the optimal tableau is given in Table 2 Table 2 x X2 51 $2 53 RHS 0 0 0 0 2. 0 480 N 10 2 70 3 1 120 0 SI 3 3 1 2 0 8 *1 3 3 30 50 1 70 3 0 1 - 0 270 S3 3 3 1 1. Suppose the profit per suit is increased to RM 68. Will this change the optimal production quantities? What can be said about the change in total profit? 2. Suppose the profit per abaya is increased by RM 13. Will this change the optimal production quantities? What can be said about the change in total profit? 3. Suppose a worker in the packaging department took 5 hours time-off. How much would this affect total profit? Would it change the optimal production quantities? 4. A new worker has been hired at a cost of RM 20/hour who is trained to do both cutting and sewing. The worker can work up to three hours and she can split her time between these two departments. Based on the sensitivity report, is it wise for the company to have the new worker split her time equally between cutting and sewing, or would some other plan be better? How much would this affect total profit