A vegetable farmer sells three different vegetable packages The three packages are made up as follows Package A 1 cucumber and 3 tomatoes Package B 1 broccoli 2 cucumbers and 2 tomatoes Package C 2 broccoli and 2 cucumbers Suppose you would like to order some number of each of the three packages so that you ultimately get 20 broccoli 40 cucumber and as few tomatoes as possible a Let a represent the number of tomatoes you end up getting from your order Set up a system of equations whose solution would determine the number of each of the three packages you should order to get 20 broccoli 40 cucumber and a tomatoes b Now write down the augmented matrix associated with the system of equations from a c Use elementary row operations to obtain the RREF of the augmented matrix from b d What is the smallest number of tomatoes you will have to buy in order to get 20 broccoli and 40 cucumber Explain your answer