Name _______________________________
Lab #4 – Chapter 6 – Applications of Matrices
Read each problem carefully and show your work! Write neatly and in pencil.
Problem #1
The Collin Freight Company has an order for three products to be delivered to a
destination. Product I requires 10 cubic feet, weighs 10 pounds, and has a value
of $100. Product II requires 8 cubic feet, weighs 20 pounds, and has a value of $20.
Product III requires 20 cubic feet, weighs 40 pounds, and has a value of $200. If the
carrier can carry a total of 6,000 cubic feet, 11,000 pounds, and is insured for $36,900,
how many of each product can be carried?
a) Fill out the following table from the information given:
Product I
Product II
Product III
Volume (cu.ft)
Weight (lb)
Value ($)
b) Let x = the amount of Product I that can be carried,
y = the amount of Product II that can be carried, and
z = the amount of Product III that can be carried.
Write the system of equations to be solved.
Total
c) Write the augmented matrix for the system of equations and solve using Gaussian
Elimination. Show your work!
d) Complete the sentence:
The Collin Freight Company can carry __________ of Product I, _________ of
Product II, and _________ of Product III.
Problem #2
A nutritionist in a nursing home is to arrange a special diet composed of three basic
foods. The diet is to include exactly 340 units of calcium, 180 units of iron, and 220
units of vitamin A. The number of units per ounce of each special ingredient for
each of the foods is indicated in the table below. How many ounces of each food
must be used to meet the dietary requirements?
a) Fill out the following table from the information given:
Food I
Food II
Food III
Calcium
30
10
20
Iron
10
10
20
Vitamin A
10
30
20
b) Let x = the number of ounces of Food I,
y = the number of ounces of Food II, and
z = the number of ounces of Food III.
Write the system of equations to be solved.
Total Units
c) Write the augmented matrix for the system of equations and solve using Gaussian
Elimination. Show your work!
d) Complete the sentence:
The dietician should give the patient __________ oz of Food I, _________ oz of
Food II, and __________ oz of Food III.