I need help with a question from my college math class.

Question

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,z.

b) fill out the table from the 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?

Answer 1

Divide row1 by 10

1	4/5	2	600
10	20	40	11000
100	20	200	36900

Add (-10 * row1) to row2

1	4/5	2	600
0	12	20	5000
100	20	200	36900

Add (-100 * row1) to row3

1	4/5	2	600
0	12	20	5000
0	-60	0	-23100

Divide row2 by 12

1	4/5	2	600
0	1	5/3	1250/3
0	-60	0	-23100

Add (60 * row2) to row3

1	4/5	2	600
0	1	5/3	1250/3
0	0	100	1900

Divide row3 by 100

1	4/5	2	600
0	1	5/3	1250/3
0	0	1	19

Add (-5/3 * row3) to row2

1	4/5	2	600
0	1	0	385
0	0	1	19

Add (-2 * row3) to row1

1	4/5	0	562
0	1	0	385
0	0	1	19

Add (-4/5 * row2) to row1

1	0	0	254
0	1	0	385
0	0	1	19

At least 254, 385 and 19 of each product can be carried.