PRODUCTION PLANNING OPTIMIZATION AND SALES BUDGETING USING LAGRANGE MULTIPLIER IN WOVEN STRAPPING CRAFTS

Abstract

UKM Tunas Harapan produces woven strapping products such as shopping baskets, along-along, mats, and pots with distribution areas such as Riau, North Sumatra, West Sumatra, Jambi, and Aceh. UKM find it difficult to plan the amount of production and control sales so that they often overproduce, which causes profits to be not maximized. The research objectives are calculating the optimal production amount and allocation to each distribution area, making an optimal sales budget plan, and calculating the profit obtained using the Lagrange multiplier method. The optimal number of production results for each product per period: 1878 shopping baskets, 1983 along-along, 283 mats, and 1425 pots. The allocation for each distribution area of each product in 1 year is Riau: 4662 shopping baskets, along- 4807 along, 837 mats, and 3658 pots. West Sumatra: 4445 shopping baskets, 5097 along-along, 841 mats, 3262 pots. North Sumatra: 5023 shopping baskets, 5608 along-along, 714 mats, 4017 pots. Jambi: 4198 shopping baskets, 4197 along-along, 615 mats, 3743 pots. Aceh: 4211 shopping baskets, 4092 along-along, 417 mats, pots, as many as 2421. While the optimal sales budget is Rp. 3,496.856,390 with the total profit obtained Rp. 1,748,394,343 the percentage of profit is 49.99%.