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 6,000 cubic feet, 11,000 pounds, and is insured for $36,900, how many of each product can be carried?

a) Identify the variables of the problem using x,y, and z.

b) fill out the following table from the information given:

x y z total

volume (cu. ft.)

weight (lb.)

value($)

c) write the augmented matrix for the system of equations

d) solve the system of equations using Gauss-Jordan Elimination.

e) In at least one complete sentence, answer the question: How many of each product can be carried?