53. Car rental patterns A car rental agency in a major city has a total of 2200 cars that it rents from three loca- tions: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return pat- terns are shown in the table (note that Airport means Metropolis Airport). Rented from Returned to AP DT CA Airport (AP) Downtown (DT) 90% 10% 10% 5% 80% 5% At the beginning of a week, how many cars should be at each location so that same number of cars will be there at the end of the week (and hence at the start of the next week)?

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53. Car rental patterns A car rental agency in a major city
has a total of 2200 cars that it rents from three loca-
tions: Metropolis Airport, downtown, and the smaller
City Airport. Some weekly rental and return pat-
terns are shown in the table (note that Airport means
Metropolis Airport).
Rented from
Returned to
АР
DT
CA
Airport (AP)
Downtown (DT)
90%
10%
10%
5%
80%
5%
At the beginning of a week, how many cars should be at
each location so that same number of cars will be there
at the end of the week (and hence at the start of the
next week)?
54. Nutrition A psychologist studying the effects of
nutrition on the behavior of laboratory rats is feeding
one group a combination of three foods: I, II, and III.
Each of these foods contains three additives, A, B, and
C, that are being used in the study. Each additive is a
certain percentage of each of the foods as follows:
Foods
II
II
Additive A
10%
30%
60%
Additive B
Additive C
0%
4%
5%
2%
2%
12%
If the diet requires 53 g per day of A, 4.5 g per day of B,
and 8.6 g per day of C, find the number of grams per
day of each food that must be used.
55. Nutrition The following table gives the calories, fat,
and carbohydrates per ounce for three brands of cereal.
How many ounces of each brand should be com-
bined to get 443 calories, 5.7 g of fat, and 113.4 g of
carbohydrates?
Cereal
Calories
Fat (g)
Carbohydrates (g)
All Fiber
50
22.0
Frosted Puffs
108
0.1
25.7
Natural
Mixed Grain
127
5.5
18.0
56. Investment A brokerage house offers three stock port-
folios. Portfolio I consists of 2 blocks of common stock
and 1 municipal bond. Portfolio II consists of 4 blocks
of common stock, 2 municipal bonds, and 3 blocks
| =| క్రీ కి ్షీ
Transcribed Image Text:53. Car rental patterns A car rental agency in a major city has a total of 2200 cars that it rents from three loca- tions: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return pat- terns are shown in the table (note that Airport means Metropolis Airport). Rented from Returned to АР DT CA Airport (AP) Downtown (DT) 90% 10% 10% 5% 80% 5% At the beginning of a week, how many cars should be at each location so that same number of cars will be there at the end of the week (and hence at the start of the next week)? 54. Nutrition A psychologist studying the effects of nutrition on the behavior of laboratory rats is feeding one group a combination of three foods: I, II, and III. Each of these foods contains three additives, A, B, and C, that are being used in the study. Each additive is a certain percentage of each of the foods as follows: Foods II II Additive A 10% 30% 60% Additive B Additive C 0% 4% 5% 2% 2% 12% If the diet requires 53 g per day of A, 4.5 g per day of B, and 8.6 g per day of C, find the number of grams per day of each food that must be used. 55. Nutrition The following table gives the calories, fat, and carbohydrates per ounce for three brands of cereal. How many ounces of each brand should be com- bined to get 443 calories, 5.7 g of fat, and 113.4 g of carbohydrates? Cereal Calories Fat (g) Carbohydrates (g) All Fiber 50 22.0 Frosted Puffs 108 0.1 25.7 Natural Mixed Grain 127 5.5 18.0 56. Investment A brokerage house offers three stock port- folios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks | =| క్రీ కి ్షీ
of preferred stock. Portfolio III consists of 7 blocks of
common stock, 3 municipal bonds, and 3 blocks of pre-
ferred stock. A customer wants 21 blocks of common
stock, 10 municipal bonds, and 9 blocks of preferred
stock. How many units of each portfolio should be
offered?
57. Investment Suppose that portfolios I and II in Problem
56 are unchanged and portfolio III consists of 2 blocks
of common stock, 2 municipal bonds, and 3 blocks of
preferred stock. A customer wants 12 blocks of com-
mon stock, 6 municipal bonds, and 6 blocks of pre-
ferred stock. How many units of each portfolio should
be offered?
Transcribed Image Text:of preferred stock. Portfolio III consists of 7 blocks of common stock, 3 municipal bonds, and 3 blocks of pre- ferred stock. A customer wants 21 blocks of common stock, 10 municipal bonds, and 9 blocks of preferred stock. How many units of each portfolio should be offered? 57. Investment Suppose that portfolios I and II in Problem 56 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of com- mon stock, 6 municipal bonds, and 6 blocks of pre- ferred stock. How many units of each portfolio should be offered?
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