Homework 13. Number of Children Proportion of Families 10.2% 15.9% 31.8% 42.1%

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1 Homework 8... Raffles: In a raffle tickets are being sold at $. each. The first prize is $. There are second prizes of $5 each, and 5 third prizes of $ each (there are 8 prizes in all). Jenn bus ticket. How much more than the epected value of the ticket does she pa? 8... A fair coin is tossed times, and a plaer wins $ if tails occur, wins $ if tails occur, and loses $ if no tails occur. If tail occurs, no one wins. (a) What is the epected value of the game? (b) Is the game fair? (c) If the answer to part (b) is No, how much should the plaer win or lose for a toss of eactl tail to make the game fair? 8... Colleen bets $ on a -digit number. She wins $75 if she draws her number from the set of all -digit numbers. {,,,..., 99}; otherwise, she loses her $. (a) Is this game fair to the plaer? (b) How much is Colleen epected to lose in a game? 8... Two teams have plaed each other 4 times. Team A won 9 games, and team B won 5 games. The will pla again net week. Bob offers to bet $ on team A while ou bet $4 on team B. The winner gets the $. Is the bet fair to ou in view of the past records of the two teams? Eplain ou answer A department store wants to sell purses that cost the store $4 each and purses that cost the store $ each. If all purses are wrapped in 4 identical boes and if each customer picks a bo randoml, find (a) Each customer s epectation. (b) The department store s epected profit if it charges $5 for each bo Sarah draws a card from a deck of 5 cards. She receives 4 cents for a heart, 5 cents for an ace, and 9 cents for the ace of hearts. If the cost of a draw is 5 cents, should she pla the game? Eplain Famil Size: The following data give information about famil size in the United States for a household containing a husband and wife where the husband is in the -4 age bracket: Number of Children Proportion of Families.% 5.9%.8% 4.% A famil is chosen at random. Find the epected number of children in the famil.

2 (In problems -4 find the maimum and minimum values (if possible) of the given objective function subject to the constraints.)..5. z 5... Optimal Land Use: A farmer has 7 acres of land available on which to grow some sobeans and some corn. The cost of cultivation per acre, the workdas needed per acre, and the profit per acre are indicated in the table: Sobeans Corn Total Available Cultivation Cost $ $ $8 Per Acre Das of Work das 4 das das Per Acre Profit per Acre $ $5 As indicated in the last column, the acreage to be cultivated in limited b the amount of mone available for cultivation costs and b the number of working das that can be put into this part of the business. Find the number of acres of each crop that should be planted in order to maimize the profit.... Investment Strateg: An investment broker wants to invest up to $,. She can purchase a tpe A bond ielding a % return on the amount invested and she can purchase a tpe B bond ielding a 5% return on the amount invested. She also wants to invest at least as much in the tpe A bond as in the tpe B bond. She will also invest at least $5 in the tpe A bond and no more than $8 in the tpe B bond. How much should she invest in each tpe of bond to maimize her return?... Manufacturing: A factor manufactures two products, each requiring the use of three machines. The first machine can be used at most 7 hours; the second machine at most 4 hours; and the third machine at most 9 hours. The first product requires hours on machine, hour on machine, and hour on machine ; the second product requires hour each on machines and, and hours on machine. If the profit is $4 per unit for the first product and $ per unit for the second product, how man units of each product should be manufactured to maimize profit? Homework 4

3 (In Problems - graph each inequalit) Without graphing, determine which of the points P (9, 5), P (, 4), P (4,) are part of the graph of the following sstem: 4 5 (In Problems 7-8 graph each sstem of linear inequalities. Tell whether the graph is bounded or unbounded and list each corner point of the graph.) (In Problems - the given figure illustrates the graph of the set of feasible points of a linear programming problem. Find the maimum and minimum values of each objective functions.)... z (Use the graphic below)

4 8 (,7) (7,8) 4 (,) (8,) 4 8 (In Problems 7-4 maimize (if possible) the quantit z 5 7 subject to the given constraints.) Diet: A diet is to contain at least 4 units of vitamins, 5 units of minerals, and 4 calories. Two foods are available: F, which costs $.5 per unit, and F, which costs $. per unit. A unit of food F contains units of vitamins, unit of minerals, and 4 calories; a unit of food F contains unit vitamins, units of minerals, and 4 calories. Find the minimum cost for a diet that consists of a miture of these two foods and also meets the minimal nutrition requirements...5. Investment Strateg: A financial consultant wishes to invest up to a total of $, in two tpes of securities, one that ields % per ear and another that ields 8% per ear. Furthermore, she believes that the amount invested in the first securit should be at most one-third of the amount invested in the second securit. What investment program should the consultant pursue in order to maimize income?... Scheduling: Blink appliances has a sale on microwaves and stoves. Each microwave requires hours to unpack and set up, and each stove requires hour. The storeroom space is limited to 5 items. The budget of the store allows onl 8 hours of

5 emploee time for unpacking and setup. Microwaves sell for $ each, and stoves sell for $ each. How man of each should the store order to maimize revenue?..7. Cost Control: An appliance repair shop has 5 vacuum cleaners, TV sets, and 8 VCRs to be repaired. The store emplos two part-time repairmen. One repairman can repair one vacuum cleaner, three TV sets, and three VCRs in week, while the second repairmen can repair one vacuum cleaner, two TV sets and si VCRs in week. The first emploee is paid $5 a week and the second emploee is paid $ a week. To minimize the cost, how man weeks should each of the two repairmen be emploed? Homework 5 (In Problems 9-5 solve each sstem of equations b finding the reduced row-echelon form of the augmented matri. If there is no solution, sa the sstem is inconsistent.) z z z z z z z 5 z z z z

6 ..5. z z 4 z..5. z z z..5. Miing Chemicals: A chemistr laborator has available three kinds of hdrochloric acid (HCl): %, %, and 5% solutions. How man liters of each should be mied to obtain liters of 5% HCl? Provide a table showing at least si of the possible solutions Repeat Problem 5 if the miture is to be liters of 4% HCl. Homework : Dependent Sstem Handout Homework 7 (In Problems - tell whether the given matri is in reduced row-echelon form.)

7 (In Problems -8 the reduced row-echelon form of the augmented matri of a sstem of linear equations is given. Tell whether the sstem has one solution, no solution, or infinitel man solutions.)

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9 ..7. (In Problems - write the dimension of each matri.) (In Problems -4 determine whether the given statements are true or false, tell wh.) is square is if =

10 (In Problems -5 use the matrices below. For Problems -44 perform the indicated operation(s); for Problems 45-5 verif the indicated propert.).4.5. A C.4.4. A 5( B C ) Homework 8: Test II Handout