I have been having much difficulty understanding matrices and a group of us have become desperate to find some comprehension of this problem. We have come up with an answer for c, but still not sure if it's correct. If you could please be of assistance it would be greatly appreciated!
A company makes three types of product (A,B, and C) with specifications below:
Product | A | B | C | Total Allowed
Weight 20 20 60 220 lbs
Volume 20 15 20 125 cu ft
a) Write a system of equations that could be used to determine what combination of products should be shipped.
b) Write the augmented matrix that matches the system.
c) Perform row operations to obtain a reduced matrix.
d) Interpret the matrix to determine the quantities to be shipped.
A) You have products (I'm going to say items for future reference so you don't mix it up with multiplication) A, B, C, and D. Item A has weight 20 and volume 20, item B has weight 20 and volume 15, etc. Your combination of items will be A + B + C + D = sum of some quantity.
B) The system you're solving requires two conditions: that the total weight combined of 3 items, are to equal 220 lb -AND- the total volume of the 3 items is 125 cuft. Using the equations above, you have 2 equations and 3 variables. You are now able to write such an augmented matrix using the coefficients.
C) This one I believe you will know how to do once you find B.
D) Look at the values of A, B, and C you have for your system. You will have one parameter because you only have 2 equations for 3 variables. Now, be careful, since these are not just arbitrary numbers but represent physical quantities, you can't have negative quantities, so scale accordingly. In other words, there is a minimum and maximum "allowed" value for your numerical parameter.