3f-+linear+programming

Linear programming: For more practice problems go here:   http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-825178-4&chapter=3&lesson=5 For help in general go here:   1. http://regentsprep.org/Regents/math/ALGEBRA/AE9/GrIneqTR.htm 2. http://www.purplemath.com/modules/linprog2.htm (SORRY THE GREATER/LESS THAN SIGNS DONT REALLY WORK) 1. Find the maximal and minimal value of //z// = 2//x// + 4//y// subject to the following constraints: { x + 2y is less than or equal to 14 } { 3x - y is great than or equal to 0 } { x - y is less than or equal to 2 } Answers: vertices- (2,6) (6,4) (-1,-3)    maximum - z = 34 minimum - z = -15 For these types of problems, you will receive some form of information through words, but don't worry its not exactly a word problem. Either you are given variables or you have to make them yourself. After you have your variables, you need to make an objective quantity which is the total number or amount you want to make, etc. Next are the constraints, which you make based on the information you receive in the problem. When you have your constraints, you then graph them and figure out your objective quantity based on the points that are inside the constraints. You then need to find all the vertices of your feasible region. After you find the vertex coordinates, plug to x and y's into your objective constraint and you will find the profit, total, etc that you are looking for. 2. A shoe company makes sneakers and sandals. Variables: x= number of pairs of sandals made in a day y= number of pairs of sneakers made in a day Objective Quantity: The company makes 30 dollars for every pair of sandals and 20 dollars for every pair of sneakers. The company is interested in maximizing profit. Write the Objective Quantity: Constraints: 1. It takes 1 piece of leather to make a pair of sandals and 3 pieces of leather to make a pair of sneakers. The factory can use at most 147 pieces of leather a day. What is the constraint? 2. The company limits production to at most 74 pair of shoes a per day. What is the constraint? 3. Sandals require a special buckle, which means you can't make more than 50 pairs of sandals per day. What is the constraint? 4. The owner wants to make sure he produces enough sandals. He has demanded that the factory make at least 6 pairs of sandals per day. What is the constraint? 5. Of course, it doesn't make sense to consider a negative number of sneakers. What is the constraint? To find a vertice that is non-trivial, use two constraints to figure out x and y. Answers: Obj. Quantity= 30x+20y=P Constraints: 1. 1x+3y is less than or equal to 147 2. x+y is less than or equal to 75 3. x is less than or equal to 50 4. x is greater than or equal to 6 5. y is greater than or equal to 0

Vertices: Value of Profit at that vertex: (50,0) 1,500 (6,0) 180 (50,25) 2,000 (39, 36) 1,890 (6, 47) 1,120   