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# FINITE MATH & ITS APPLIC MA 162

UK

GPA 3.54

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This 4 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 162 at University of Kentucky taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/228160/ma-162-university-of-kentucky in Mathematics (M) at University of Kentucky.

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Date Created: 10/23/15

MA162 Review 2 The following topics and skills will be examined in the second midterm test 0 Graphing the feasible set of a system of linear inequalities in two variables Finding corner points 0 Formulating written descriptions of feasible sets as linear inequalities 0 Solving linear programs by graphical7 corner point and simplex methods 0 Formulate word problems as linear programs 0 The augmented coordinate system 0 The simplex tableau Basic and nonbasic variables7 choosing the pivot element7 finding the augmented coordinates of a corner point and determining ifa tableau corresponds to the optimal feasible point 0 Dual prices7 righthand side ranging and changing coef cients in objective func tion Below are some sample questions to help you prepare for the exam Be sure that you understand all of the topics from the above list7 not just the topics covered by the questions below In your answers on the exam7 please be sure to 1 Check answers when possible 2 Clearly indicate your answer and the reasoning used to arrive at that answer 3 Label all variables and equations 1 a Solve the following linear program by the graphical method max m2y st my 4 2924 3136 93203120 b Check your answer by re solving the problem by the corner point method 2 The feasible set for the following system of linear inequalities is sketched below m y 0 5034 631 g 30 y S 02207 920 y Xy0 5 A B y4 C 3 E O 2 1 5X6y30 D I I I I I v 1 2 3 4 5 6 X a Rewrite the system of inequalities by introducing slack variables b Find the augmented coordinates of the points labelled A E 3 You own a shipping company which transports two types of packages7 A and B Your plane can carry only 100 units of volume and 60 units of weight You know that a package of type A has a volume of 5 units and a weight of 1 unit7 but will give a profit of 3 a package A package of type B has a volume of 2 units and a weight of 2 units and gives you a profit of 2 per package Customs will allow you to transport no more than 16 packages of type A per ight How many of each type package should you transport to maximize your profit What is the maximum profit 4 a Carry out one simplex pivot on the following tableau P 031 032 91 92 HHS 1 1 2 0 0 0 0 1 1 1 0 4 0 2 4 0 1 8 After you have done the pivot7 answer the following questions i Are we done with the problem7 that is have we reached an optimal solution Why or why not ii Find the associated corner point b Carry out one pivot so that the variable 032 becomes basic Remark There are two possible ways to do this 031 032 033 91 92 93 HHS 1 1 0 0 1 2 4 0 3 0 1 1 0 3 0 0 1 0 2 1 2 After you have pivoted7 give the basic variables and their values What are the nonbasic variables and their values 5 Use the attached LINDO printout to answer the following questions a What is the optimal feasible point What is the maximum value of the objective function b Com ute the new value of the ob39ective function if the coef cient of as is P J decreased by 1 unit c Compute the new value of the objective function if the coef cient of as in the objective function is 8 d Compute the new value of the objective function if the righthand side of constraint 2 is increased by 10 units For this question7 assume that the coef cient of as has been returned to its original value7 4 MAX 4 X 2 Y 5 Z SUBJECT TO 2 X 2 Y 3 Z lt 30 3 3 X Y 2 Z lt 40 4 X Y Z lt 20 END LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 1 700000000 VARIABLE VALUE REDUCED COST X 8571428 0000000 Y 0000000 1000000 Z 7142857 0000000 ROW SLACK OR SURPLUS DUAL PRICES 2 0000000 1000000 3 0000000 1000000 4 4285714 0000000 NO ITERATIONS 2 RANGES IN WHICH THE BASIS IS UNCHANGED OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X 4000000 3500000 2333333 Y 2000000 1000000 INFINITY Z 5000000 6999999 1400000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 30000000 30000000 16666664 3 40000000 15000000 20000000 4 20000000 INFINITY 4285714

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