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Management science refers to operational techniques and model used by companies and individuals to solve managerial problems by providing an effective decision on the work plan. Linear programming model is model that assists organizations in solving management decision making problems by using mathematical procedures. Julia Robertson is a final year student pursuing a course in Finance at Tech and she is facing a challenge in raising her school fees.

She embarks on investigating diverse ways of financing her education in her final year. She identifies a food booth outside the Tech stadium at domicile football arena which she considers renting. Through her familiarity with the arena she discovers that fans and players of the games consume lots of food, which motivates her to start the business. The food booth is small in size, and the requirement for renting it is for her to play a game at \$1000. At the Tech property, only the Tech department is allowed to sell both food and drinks, and vendors to sell either drinks or food to the fans. Julia decides to prepare foods such as hot dogs, barbecue sandwiches and cheese pizza, because fans who watch the game at the stadium like such foods.

At the Tech stadium, fans buy food during half time and before the start of the game; this means Julia should prepare food before the game. Julia needs a warm oven to store the food which will cost her \$600. The oven contains 16 shelves; 3 feet by feet this will enable her to store food before half time and at the start of the game.

Julia’s capital is \$1,500 which is enough to prepare and purchase items. She decides to order pizza from a delivery industry at \$6 that will give 8 slices; a piece of hot dog will cost her \$0.45 and \$0.90 per barbecue. She decides to sell barbecue at \$2.25, hot dog and a slice of pizza at \$1.50. The total profit from a pizza slice \$0.75 and hot dog \$1.5. She plans to use the profit attained at the first game to purchase other ingredients to make food for the next game. In her research, she discovers that she can sell more food when she develops a client base for every period and follows the stipulate guideline.

At this point, a liner programme model is essential to assist her in making a decision whether or not to operate the business:

Lending money from friends is not advisable for Julia because the profit she gets from the first game is enough to purchase other ingredients for the next game. The first sell, therefore, is enough to expand the business without loans from friends.

Paying a friend to assist her at \$100 might lead Julia to debt, because the profit from the sale is not sufficient to pay her and buy ingredient after the first game. She can only hire an assistant after developing the client base per period and following demand guideline. The linear programme model assists individuals or groups in solving problems by offering a solution in decision making process. In the above model, the programme ambiguity is that it is not able to stipulate the number of clients expected for the business.

Therefore, Julia’s investigation on her business analyzes the business environment well enough that will lead her to a successful business. Her capital is compelling for the growth of the business if she gives quality and observes time to maintain her customers. Julia should continuously use the linear programme model to make a clear decision on how to develop her business.

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