Practice Problems_LP_Formulation.pdf - BU275 Practice problems for Linear Programming Formulation 1 1 Fred Jonasson manages a family-owned farm To

Practice Problems_LP_Formulation.pdf - BU275 Practice...

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BU275 Winter 2018 BU275: Practice problems for “Linear Programming: Formulation” 1 1) Fred Jonasson manages a family-owned farm. To supplement several food products grown on the farm, Fred also raises pigs for market. He now wishes to determine the quantities of the available types of feed (corn, tankage, and alfalfa) that should be given to each pig. Since pigs will eat any mix of these feed types, the objective is to determine which mix will meet certain nutritional requirements at a minimum cost. The number of units of each type of basic nutritional ingredient contained within a kilogram of each feed type is given in the following table, along with the daily nutritional requirements and feed costs. Formulate a linear programming model for this problem. 2) On their farm, the Friendly family grows apples that they harvest each fall and make into three products apple butter, applesauce, and apple jelly. They sell these three items at several local grocery stores, at craft fairs in the region, and at their own Friendly Farm Pumpkin Festival for 2 weeks in October. Their three primary resources are cooking time in their kitchen, their own labor time, and the apples. They have a total of 500 cooking hours available, and it requires 3.5 hours to cook a 10-gallon batch of apple butter, 5.2 hours to cook 10 gallons of applesauce, and 2.8 hours to cook 10 gallons of jelly. A 10-gallon batch of apple butter requires 1.2 hours of labor, a batch of sauce takes 0.8 hour, and a batch of jelly requires 1.5hours. The Friendly family has 240 hours of labor available during the fall. They produce about 6,500 apples each fall. A batch of apple butter requires 40 apples, a 10-gallon batch of applesauce requires 55 apples, and a batch of jelly requires 20 apples. After the products are canned, a batch of apple butter will generate $190 in sales revenue, a batch of applesauce will generate a sales revenue of $170, and a batch of jelly will generate sales revenue of $155. The Friendlys want to know how many batches of apple butter, applesauce, and apple jelly to produce in order to maximize their revenues. Formulate a linear programming model for this problem. 3) The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products, Products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table: 1 Questions are based on “Introduction to Management Science”, Hillier and Hillier, 5th edition, McGraw Hill, and on “Introduction to Management Science”, Taylor, 12th edition, Pearson.
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BU275 Winter 2018 The number of machine-hours required for each unit of the respective products are shown in the next table.
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  • Winter '13
  • HosseinZolfagharinia

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