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	Total
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.

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.

2.

Math 1314 von Holstein

A concession stand at a city park sells hamburgers, hot dogs, and drinks. Three patrons buy the food and drink combinations denoted in the following table. Patron 1 spends $11, patron 2 pays $5 for the food, and the price of the food for patron 3 is $22. Let x, y and z represent the cost for a hamburger, a hot dog, and a drink, respectively. Set up a system of equations to solve for x, y and z. Then, set up the augmented matrix for the system and solve the system.

Math 1314 von Holstein

Patron	Hamburgers	Hot Dogs	Drinks
1	1	1	5
2	0	1	2
3	3	1	11

a.) Determine the system of equations to be solved.

b.) Set up the augmented matrix for the system.

c.) Solve the system of equations using Gauss-Jordan Elimination. Please also show the initial matrix, row operations in order, and the final matrix for credits. State the solution properly.