Math Finite Mathematics Instructor - Dalip Sondhi Exam 1

Transcription

1 Math - Finite Mathematics Instructor - Dalip Sondhi Eam Name Date PLEASE SUBMIT THIS TEST, SUMMARIZE YOUR ANSWERS ON IT, STAPLE YOUR SUPPORTING WORK TO IT & SCANTRON INSERTED BEHIND PAGE, UNSTAPLED. GRADING RUBRIC: 0% FOR CORRECT ANSWERS, 30% FOR COMPLETE & CORRECT SUPPORTING WORK, 0% FOR NEAT & PROFESSIONAL WORK. DUE DATE: MAR, 0. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write an equation for the line. Use slope-intercept form, if possible. ) Through (-3, -), m = = = - 8 = + = - + Determine the equation of the line described. Put answer in the slope-intercept form, if possible. ) Through (, ), perpendicular to = = = = = Use the echelon method to solve the sstem. 3) = - = (-, -8) (, 8) (, -8) (-, 8) Use the echelon method to solve the sstem of three equations in three unknowns. ) + + z = - - z = + + z = (-,, ) (,, -) (, -, ) No solution Solve the sstem of equations. Let z be the parameter. ) z = z = (-8 + z, 8 + z, z) 9 - z, - z, z ) ) 3) ) ) 9 - z, + z, z 9 - z, z, z ) Anne and Nanc use a metal allo that is.% copper to make jewelr. How man ounces of a 3% allo must be mied with a 30% allo to form 70 ounces of the desired allo? 8 ounces ounces ounces 9 ounces )

2 Write the augmented matri for the sstem. Do not solve. 7) + - z = z = z = ) Write the sstem of equations associated with the augmented matri. 00-8) = 0 = -3 z = - = - = z = 3 Use the indicated row operation to change the matri. 9) Replace R b R + R. = = - z = -3 = -8 = - z = 0 8) 9) Use the Gauss-Jordan method to solve the sstem of equations. 0) z = z = z = 0 (-3,, ) (3, 8, ) (3,, 8) No solution 0) ) z = z = + + z = z + -z +, -z - 7, z, -z - 7, z -z +, -z + 7, z z -, z - 7, z ) ) - + 8z = = + + 8z = -80 (, 8, -) (, 8, 7) (, 8, 0) No solution )

3 Write a matri to displa the information. ) At a store, Sam bought 3 batteries, 0-watt light bulbs, 00-watt light bulbs, 8 picture-hanging kits, and a hammer. Jennifer bought batteries, 3 00-watt light bulbs, and a package of tacks. Write the information as a matri ) Find the values of the variables in the matri. ) z 0 3m = - 8 3a 37 0 =, = -, a = /3, z = /9, m = 0 =, =, a = /3, z = /9, m = 0 =, =, a = /3, z = /9, m = 0 =, =, a = 3, z = 9, m = 0 ) ) Let A = 0 0 and B = 0 -. Find A + B ) Find the matri product, if possible ) Does not eist ) Find the inverse, if it eists, for the matri ) )

4 Solve the sstem of equations b using the inverse of the coefficient matri z = 8) - z + w = z + w = -0-3z + w = -7 (0, -, 0, -) (-, -,, -) (-, 0,, -3) (-, -,, -) 9) A basketball fieldhouse seats,000. Courtside seats cost $8, endzone seats cost $7, and balcon seats cost $. The total revenue for a sellout is $88,000. If half the courtside seats, half the balcon seats, and all the endzone seats are sold; then the total revenue is $,000. How man of each tpe of seat are there? 800 endzone 3000 courtside 000 balcon 8000 balcon 0) Suppose the following matri represents the input-output matri of a simplified econom that involves just three commodit categories: manufacturing, agriculture, and transportation. How man units of each commodit should be produced to satisf a demand of 900 units for each commodit? 8) 9) 0) Mfg Agri Trans Mfg 0 / / Agri / 0 / Trans /3 / 0 9 units of manufacturing, 0 units of agriculture, and 097 units of transportation units of manufacturing, 38 units of agriculture, and 097 units of transportation 9 units of manufacturing, 097 units of agriculture, and units of transportation 0 units of manufacturing, 097 units of agriculture, and 9 units of transportation

5 Graph the feasible region for the sstem of inequalities. ) )

6 ) ) Write the sstem of inequalities that describes the possible solutions to the problem. 3) An airline with two tpes of airplanes, P and P, has contracted with a tour group to provide transportation for a minimum of 00 first class, 70 tourist class, and 00 econom class passengers. Airplane P can accommodate 0 first class, 0 tourist class, and 0 econom class passengers. Airplane P can accommodate 8 first class, 30 tourist class, and econom class passengers. Let represent the number of planes of tpe P and represent the number of planes of tpe P , , z z 70 0, , 0 3)

7 Use the indicated region of feasible solutions to find the maimum and minimum values of the given objective function. ) z = - 0 ) (0, ) (., ) (, 0) Maimum of 7; minimum of 0 Maimum of -0; minimum of 0 Maimum of -8.; minimum of -0 Maimum of 7; minimum of -0 Use graphical methods to solve the linear programming problem. ) Maimize z = 8 + subject to: ) Maimum of 0 = 8 Maimum of 00 when = 8 Maimum of 9 when = Maimum of 9 when = ) A compan makes two kinds of engineering pencils, Tpe I and Tpe II (delue). Tpe I needs min of sanding and min of polishing. Tpe II needs min of sanding and 3 min of polishing. The sander can run no more than hours per week and the polisher can run no more than 73 hours a week. A $3 profit is made on Tpe I and $ profit on Tpe II. How man of each tpe should be made to maimize profits? 730 Tpe I, 0 Tpe II 00 Tpe I, 7 Tpe II 0 Tpe I, 79 Tpe II 7 Tpe I, Tpe II Write the solutions that can be read from the simple tableau. 7) 3 s s z s = 7, =, z = 9;, 3, s = 0 s = 7, =, z = 9;, 3, s = 0 s = 7, =, z = 9;, 3, s = 0 s = 7, =, z = 9;, 3, s = 0 ) 7) 7

8 Pivot once about the circled element in the simple tableau, and read the solution from the result. 8) 8) = 3, =, z = -7; 3, s, s = 0 = 3, s = -, z = -7;, 3, s = 0 = 3, = -, z = ; 3, s, s = 0 = 9, = -, z = -7;, 3, s = 0 9) Jerr builds rocking chairs and porch swings and sells them a a local flea market. The lumber requirements for each tpe of item are summarized in the table below. Rocking Chair Porch Swing 's 's 's 3 Currentl, Jerr has 00 's, 's, and 00 's in stock. Rocking chairs sell for $0 and porch swings sell for $8. How man pieces of each tpe of lumber are left over after Jerr has built the number of chairs and swings that maimize his revenue? 's, 0 's, and 0 's. 's, 0 's, and 's. 0 's, 0 's, and 's. 's, 0 's, and 's. 9) 8