SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Math 132 Eam 2 Review (.1 -.5, ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the given ordered set of numbers is a solution of the sstem of equations. 1) (3, -3) + = = -3 1) 2) (-3, -2, -) z = 3 + z = z = -1 2) Solve the sstem of two equations in two variables. 3) + = = 21 3) ) 3-2 = = 1 ) 5) = = 20 5) Multipl both sides of each equation b a common denominator to eliminate the fractions. Then solve the sstem. ) = 7 ) = Solve the problem b writing and solving a suitable sstem of equations. 7) A shopkeeper orders 2 pounds of cashews and peanuts. If the amount of cashews he orders is 2 pounds less than the amount of peanuts, how man pounds of peanuts did he order? 7) Solve the sstem b back substitution. 8) z = z = -0 2z = - 8) Solve the sstem of equations. If the sstem is dependent, epress solutions in terms of the parameter z. 9) + + z = -7 9) - + z = z = -19 Perform row operations on the augmented matri as far as necessar to determine whether the sstem is independent, dependent, or inconsistent. ) - + z = 2 ) z = z = -3 1

2 11) + + z = z = z = 11) Write an augmented matri for the sstem of equations. 12) 3 + 9z = z = z = 7 12) Write the sstem of equations associated with the augmented matri. Do not solve. 0-13) ) The reduced row echelon form of the augmented matri of a sstem of equations is given. Find the solutions of the sstem. 1) 1) Solve the problem b writing and solving a suitable sstem of equations. 15) A small business takes out loans from three different banks to bu some new equipment. The total amount of the three loans is $20,000. The first bank offered an interest rate of 1%. The second bank offered a rate of 18% and the amount borrowed from this bank was $5000 less than twice as much as the amount borrowed from the first bank. The third bank offered a rate of 15%. The total annual interest was $3270. How much did the borrow from each bank? 15) 1) A basketball fieldhouse seats 15,000. Courtside seats sell for $, endzone for $, and balcon for $. Total revenue for a sell-out is $82,000. If half the courtside and balcon and all endzone seats are sold, the total revenue is $7,000. How man of each tpe are there? 1) Perform the indicated operation where possible. 17) ) 18) ) Perform the indicated operation. 19) Let C = -2. Find C. 19) 20) Let A = 23 2 and B = 0-1. Find 2A + B. 20) 2

3 Solve the problem. 21) Carne and Dobler sell home and mortgage insurance. Their sales for the months of Ma and June are given in the matrices. 21) M = Home Mortgage 22,000 5,000 Carne 17,000 27,000 Dobler J = 25,000,000 1,000 21,000 Carne Dobler Find the matri that would give the change in sales from Ma to June. 22) What is the size of the matri? ) A manufacturer of wooden chairs and tables must decide in advance how man of each item will be made in a given week. Use the table to find the sstem of inequalities that describes the manufacturerʹs weekl production. 23) Use for the number of chairs and for the number of tables made per week. The number 23) of work-hours available for construction and finishing is fied. Hours per chair Hours per table Total hours available Construction Finishing Graph the linear inequalit. 2) )

4 Graph the feasible region for the sstem of inequalities. 25) ) - - 2) ) ) )

5 Find the value(s) of the function on the given feasible region. 28) Find the minimum of z = ) 29) Find the maimum and minimum of z = ) Use graphical methods to solve the linear programming problem. 30) Maimize z = subject to: ) - - 5

6 Find the value(s) of the function, subject to the sstem of inequalities. 31) Find the maimum and minimum of P = - 2 subject to: 0 5, 0 8, , and ) State the linear programming problem in mathematical terms, identifing the objective function and the constraints. 32) A car repair shop blends oil from two suppliers. 32) Supplier I can suppl at most gal with 3.7% detergent. Supplier II can suppl at most gal with 3.3% detergent. How much can be ordered from each to get at most 0 gal of oil with maimum detergent? The Acme Class Ring Compan designs and sells two tpes of rings: the VIP and the SST. The can produce up to 2 rings each da using up to 0 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. 33) How man of each tpe of ring should be made dail to maimize the companʹs profit, if 33) the profit on a VIP ring is $20 and on an SST ring is $50? Convert the constraints into linear equations b using slack variables. 3) Maimize z = Subject to: , 2 0 3) Find the pivot in the tableau. 35) z ) Use the indicated entr as the pivot and perform the pivoting once. 3) 3) Write the basic solution for the simple tableau determined b setting the nonbasic variables equal to 0. 37) z 37)

7 Use the simple method to solve the linear programming problem. 38) Maimize z = subject to: with 1 0, ) 39) Maimize z = subject to: with 1 0, 2 0, ) A baker makes sweet rolls and donuts. A batch of sweet rolls requires 3 lb of flour, 1 dozen eggs, and 2 lb of sugar. A batch of donuts requires 5 lb of flour, 3 dozen eggs, and 2 lb of sugar. Set up an initial simple tableau to maimize profit. 0) The baker has 380 lb of flour, 300 dozen eggs, 200 lb of sugar. The profit on a batch of 0) sweet rolls is $5.00 and on a batch of donuts is $ A manufacturing compan wants to maimize profits on products A, B, and C. The profit margin is $3 for A, $ for B, and $15 for C. The production requirements and departmental capacities are as follows: Department Production requirement b product (hours) Departmental capacit (Total hours) A B C Assembling ,000 Painting ,000 Finishing ,000 1) What is the maimum profit in this model? 1) 2) What is the maimum profit if the capacit of the painting department changes to 0,000 hours? 2) Given the matrices A and B, find the matri product AB. 3) A = 1 3, B = 0 2 Find AB. 3) ) A = , B = Find AB. ) 7

8 Determine whether the two matrices are inverses of each other b computing their product ) , ) Find the inverse, if it eists, of the given matri. 0 ) ) 7) ) 8

9 Answer Ke Testname: MATH 132 EXAM 2 REVIEW 1) Yes 2) Yes 3) (0, 3) ) No solution 5) , for an real number 2 ) (, 8) 7) 33 pounds 8) (5, -3, -5) 9) (-3, -2, -2) ) Inconsistent 11) Independent 12) ) = - = z = 1) (13-3w, -9, + 2w, w) for an real number w 15) first bank $000, second bank $7000, third bank: $7000 1) 3000 courtside 2000 endzone,000 balcon 17) Not defined 18) ) ) 31 21) ) 3 23)

10 Answer Ke Testname: MATH 132 EXAM 2 REVIEW 2) ) - 2) ) ) -

11 Answer Ke Testname: MATH 132 EXAM 2 REVIEW 29) 220, 12 30) Maimum of 0 when = 8 and = 3 31) 50, -1 32) Maimize Subject to: ) 0 VIP and 2 SST 3) = = 25 35) 3 in row 2, column 3) 37) 1 = 0, 2 = 0, 3 = 29, = 0, 5 = 1, z = 19 38) Maimum is 30 when 1 =, 2 = 0 39) Maimum is 20 when 1 = 0, 2 =, 3 = 0 0) ) $225,000 2) $225,000 3) ) ) Yes ) )

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