1324 Test 2 Review Page 1 of 15 Instructor: J. Travis. 15. Graph the following linear inequalities.

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1 4 Tet Review Page of Intructor: J. Travi. Graph the following linear inequalitie. a) y b) 6+ 4y c) 4y< 6. Graph the following ytem of linear inequalitie. y a) b) + y + y 4 y

2 7. Ue graphical method to olve the linear programming problem. Page of Maimize: z = + y Subject to + y 6 4+ y 6 y, 8. Ue graphical method to olve the linear programming problem. Minimize: w= + y Subject to: + y + y y

3 9. Ue graphical method to olve the linear programming problem. Page of Maimize: z = + y Subject to 8+ 6y 84 + y y 6 y

4 Page 4 of. Write the mathematical model that would be ued to olve the problem. State clearly what i repreented by each variable. (NOTE: You do not need to olve it. Jut write the model.) a) Jamaal i planning to invet up to $, in City Bank or State Bank. He want to invet at leat $4 in City Bank, but not more than $9; ince Stat Bank doe not inure more than $,, he want to invet no more than thi amount in State Bank. The interet earned at City Bank i %, and the interet at State Bank i 7%. How much hould he invet in each bank to earn the mot interet? b) A baker ha 6 unit of flour, unit of ugar, and unit of raiin. A loaf of raiin bread require unit of flour, unit of ugar and unit of raiin, while a raiin cake need unit of flour, 4 unit of ugar and unit of raiin. If raiin bread ell for $ a loaf and a raiin cake for $4, how many of each hould be baked o that the gro income i maimized?

5 Page of. What type of problem i the imple method deigned to olve? Decribe the tep ued in the imple method.. For the following linear programming problem, write the equation repreented by the initial imple tableau, and then write the initial imple tableau. a) Maimize z = 8+ + b) Maimize z = + Subject to: ,, Subject to: ,, Equation repreented by the tableau: Equation repreented by the tableau: Initial Tableau: Initial Tableau:

6 Page 6 of. Determine the pivot element for the following imple tableau. a) b) c) d) e)

7 Page 7 of 4. For the following tableau perform one pivot on the tableau below. You mut how what row operation you performed, decribing them uing notation like thi: R4 + R R4 (for eample). 7 After your pivot: Write the value of the variable given by the new tableau. State whether an optimal olution ha been reached. (Give a Ye or No anwer.) Eplain how you determined whether or not the optimum ha been reached. a) z b) P c) P

8 . Ue the imple method to olve the following linear programming problem. Page 8 of Maimize z = + + Subject to: ,,

9 6. Given the following problem, write the dual problem. (NOTE: You do not need to olve it. Jut write the dual.) Page 9 of a) Minimize z = y+ y + y Subject to: y + y + y y + y + 4y y + y + y 6 y, y, y b) Minimize w= + 4 Subject to: ,

10 7. Solve the following linear programming problem by duality. Page of Minimize w= + 4 Subject to: , 8. The tableau below i the finihed tableau for the dual of the minimization problem involving an objective function and deciion variable,, and. Write the olution to the dual problem and the original problem. (Give the value of the variable.) a) Solution to the dual problem: y y y z 9 z = y = y = y = Solution to original minimization problem: z = = = = b) y y P Solution to the dual problem: P = y = y = Solution to original minimization problem: P = = = =

11 You hould know the following formula and when to ue them. r n I = Prt A P( rt) A P r = + = ( + ) ( ) m m r = + e m Page of FV ( i) n + = PMT i PV ( i) n + = PMT i 9. Anne Kelly borrowed $,9 from her father to tart a flower hop. She repaid him after month, with interet of 8.4%. Find the total amount he repaid. How much interet did he pay? (Round to the nearet cent.). An account inveted in a money market fund grew from $67,8. to $67,9.9 in a month. What wa the interet rate? (Round to two decimal place). If Sam inveted $9, at 6.% compounded quarterly, how much would he have after four year? How much would he have if it had been compounded monthly? (Round to the nearet cent.)

12 Page of. Find the effective rate of interet for.% compounded quarterly. (Round to two decimal place). Suppoe the general rate of inflation in the economy average 8% per year. How many year would it take for the overall level of price to double? To triple? To quadruple? (Round to the nearet whole number.) 4. The parent of a newborn baby plan to make monthly payment into a college aving account o that $9, will be available on the baby th birthday. If the account pay.% compounded monthly, how much hould the parent depoit each month? (Round to the nearet cent)

13 Page of. At the end of each quarter, a -year-old woman put $ in a retirement account that pay 7% interet compounded quarterly. When he reache age 6, he withdraw the entire amount and place it in a mutual fund that pay 9% interet compounded monthly. How much i in the account when he reache age 6? How much interet ha he earned? (Round to the nearet cent.) 6. Ron Hampton i aving for a computer. At the end of each month, he put $6 in a aving account that pay 4.% interet compounded monthly. How much i in the account after year? How much interet did he earn? (Round to the nearet cent.)

14 Page 4 of 7. John Kuhida buy a ued car coting $8. He make a $ down payment, and for the ret he agree to make payment at the end of each month for four year. He pay % interet, compounded monthly. What i the amount of each payment? How much interet will he pay? (Round to the nearet cent.) 8. Kareem Adam buy a houe for $8,. He pay $6, down and take out a year mortgage at 6.9% on the balance. Find hi monthly payment and the total amount of interet he will pay. If he decide to take out a year mortgage intead, find hi monthly payment and the total amount of interet he will pay. (Round to the nearet cent.) What are the pro and con of each choice?

15 Page of 9. Scott and Jennifer purchaed a houe 6 year ago. They financed $, for year at 6% interet. What are their monthly payment? What i the remaining balance on the mortgage? How much equity do they have? 4. Clint wihe to retire at the age of 6, receiving $4 monthly payment out of hi retirement account for year. How much hould he invet in the account each month from age to 6 to make thi poible? The account pay 7% compounded monthly.