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Matrix Word Problems

1. Medicine: Five diabetic patients in a hospital each require injections of three kinds of insulin each day. The 5x3 matrix shown below gives the amounts of the three kinds of insulin each patient requires each day. If patient 1 plans to stay 10 days, patient 2 stays 5 days, patient 3 stays 20 days, patient 4 stays 10 days, and patient 5 stays 15 days, how much of each type of insulin must the medical staff have on hand?
Patient 1 Patient 2 Patient 3 Patient 4 Patient 5
Semi-lente 10 units 40 units 30 units 20 units 10 units
lente 20 units 20 units 10 units 10 units 10 units
Ultra-insulin 30 units 5 units 5 units 20 units 10 units
2. Fast Food: A fast food company sells three specials. The number of hamburgers, french fry orders, and sodas in each special is summarized below. The day's reciept indicates that there were 300 hamburgers, 500 french fries, and 400 sodas sold. How many of each type of special were sold
Special 1 Special 2 Special 3
Hamburgers 1 0 1
French Fries 2 1 0
Sodas 1 2 0
3. Dietician Protein, carbohydrates, and fats can be obtained from three foods. Each ounce of Food I contains 5 grams of protein, 10 grams of carbohydrates, and 40 grams of fat. Each ounce of Food II contains 10 grams of protein, 5 grams of carbohydrates, and 30 grams of fat. Each out of Food III contains 15 grams of protein, 15 grams of carbohydrates, and 80 grams of fat. How many ounces of each of the three foods are required to yeild 300 grams of protein, 300 grams of carbohydrates, and 1500 grams of fat?
4. Traveling: Campus Express offers college students summer charter trips in Europe. The company flies three kinds of airplanes: the Airbus 100, the Airbus 200, and the Airbus 300. Each plane is outfitted with tourist, economy, and first-class seats. The number of each kind of seat in the three types of planes is shown below. The second chart lists the number of reservations for its July flight to France. How many of each kind of plane should the company fly to fill all the seats?
Airbus 100 Airbus 200 Airbus 300
Tourist 50 75 40
Economy 30 45 25
First Class 32 50 30


Category Number of reservations
Tourist Class 305
Economy Class 185
First Class 206
5. Pharmeceutical Jerri Smith takes a daily prescription composed of 8 units of A, 14 units of B, and 16 units of C. The generic drug capsules that contain these ingredients of each of these components is shown below. How many capsules of each drug should Jerri take daily?
Generic IGeneric IIGeneric IIIRequirements
A
2
1
3
8
units
B
3
2
5
14 units
C
2
4
2
16 units
6. Construction A building contractor accepts summer orders for 135 houses, 3 condos, and 1 high-rise building. The construction materials (in appropriate units) that go into each of these buildings are listed below. How much of each raw material will be needed for all of the summer contracts
House Condos High-Rise
Lumber
10
400
500
Glass
5
150
1000
Steel
0
50
2000
Concrete
0
100
1000
Labor
20
1000
5000
7. Production: The parts requirements for three products are summarized below.
Product 1 Product 2 Product 3
Molded Plastic 2 1 3
Fasteners 3 2 2
Units of Paint 1 2 4
For the next two weeks the parts available will be the folowing:


Week 1 Week 2
Molded Plastic 5080
EUnits of Paint 60 100
First Class 206