Briefly define the term “linear programming model.” Describe the various applications of linear programming to solve business problems.

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TEA PRODUCTION AND DISTRIBUTION IN INDIA* MANAGEMENT SCIENCE IN ACTION In India, one of the largest tea producers in the world, approximately $1 billion of tea packets and loose tea are sold. Duncan Industries Limited (DIL), the third largest producer of tea in the In- dian tea market, sells about $37.5 million of tea, almost all of which is sold in packets. DIL has 16 tea gardens, three blending units, six packing units, and 22 depots. Tea from the gardens is sent to blending units, which then mix various grades of tea to produce blends such as Sargam, Double Diamond, and Runglee Rungliot. The blended tea is transported to packing units, where it is placed in packets of different sizes and shapes to produce about 120 different product lines. For example, one line is Sargam tea packed in 500-gram cartons, another line is Double Dia- mond packed in 100-gram pouches, and so on. The tea is then shipped to the depots that supply 11,500 distributors through whom the needs of approxi- mately 325,000 retailers are satisfied. For the coming month, sales managers provide estimatesofthedemandforeachlineofteaateach depot. Using these estimates, a team of senior man- agers would determine the amounts of loose tea of each blend to ship to each packing unit, the quan- tity of each line of tea to be packed at each packing unit, and the amounts of packed tea of each line to be transported from each packing unit to the vari- ous depots. This process requires two to three days each month and often results in stockouts of lines in demand at specific depots. Consequently, a linear programming model involving approximately 7000 decision variables and 1500 constraints was developed to minimize the company’s freight cost while satisfying demand, supply, and all operational constraints. The model was tested on past data and showed that stockouts could be prevented at little or no additional cost. Moreover, the model was able to provide manage- ment with the ability to perform various what-if types of exercises, convincing them of the potential benefits of using management science techniques to support the decision-making process. *Based on Nilotpal Chakravarti, “Tea Company Steeped in OR,” OR/MS Today (April 2006)