EXAMPLES OF PROBLEMS MATH MODEL STORY (SENTENCE VERBAL)

Example 1To make a required 200 grams of bread flour and 25 grams of butter. As for the B required 100 grams of bread flour and 50 grams of butter. Flour is available only 4 kg and 1.2 kg of butter available. if the price of bread A Rp.400, 00 and the price of bread B rp. 500.00. Make mathematical models.AnswerSuppose A lot of bread and more bread = x B = y, then the other variable is the flour and butter. Thus obtained the following table:Bread variable A (x) Bread B (y) InventoriesFlour 200 grams 100 grams 4000 gramsButter 25 grams 50 grams 1200 grams

 Flour and butter most widely available 4 kg = 4,000 grams and 1.2 kg = 1,200 grams so the inequality sign ≤. From the table can be created inequalities:200 x + 100 y ≤ 4000 simplified:2x + y ≤ 40. . . (1)25 x + 50 y ≤ 1200 simplified:X + 2y ≤ 48. . . (2)Since x and y are integers that are not negative then:X ≥ 0. . . (3)Y ≥ 0. . . (4)The fourth inequality above is a requirement that must be met is called constraint functions. Price of bread A rp. 500.00 and bread B rp. 400.00, the proceeds can be formulated with Z = 400 x + 500 y: Z is called the objective function or objective function that can be maximized or minimized.


Example 2An agent intends to buy 25 pieces bike bike for supplies. Karga regular bike Rp. 600,000.00 per fruit and federal bicycle Rp. 800,000.00 each. He planned not to spend the money more than Rp. 16,000,000.00 to expect profit of Rp. 100,000.00 per fruit than a regular bike and 120,000.00 per piece of federal bike. Make mathematical models.AnswerLet x = the number of regular bike and y = the number of federal bike, you might use the following table.Variable Bicycle regular (X) Bicycle federal (Y) InventoriesNumber 1 1 25Capital 600 000 800 000 16,000,000
 Stock bikes and most capital and $ 25 pieces. 16,000,000.00. So the inequality sign ≤, so pertidaksamaannya as follows:X + y ≤ 25. . . (1)≤ 16 million + 800.000y 600.000x simplified3x + 4y ≤ 80. . . (2)X ≥ 0. . . (3) andY ≥ 0. . . (4)Objective shape + Z = 100.000x 120.000y