1. The problem statement, all variables and given/known data Original question: The Cut-Right Company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef’s knife. The Regular Set consists of 2 utility knives, 1 chef’s knife, and 1 slicer. The Deluxe Set consists of 3 utility knives, 1 chef’s knife, and 1 slicer. Their profit is $30 on a Basic Set, $40 on a Regular Set, and $60 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef’s knives, and 200 slicers. Assuming that all sets will be sold, how may of each type should be produced in order to maximize profit? What is the maximum profit? 2. Relevant equations s1, s2, s3 are slack variables x1, x2, x3 are all non-negative x1 = # of basic sets produced x2 = # of regular sets produced x3 = # of deluxe sets produced 2*x1 + 2*x2 + 3*x3 + s1 = 800 x1 + x2 + x3 + s2 = 400 x2 + x3 + s3 = 200 a is the profit function given by: a = 30*x1 + 40*x2 + 60*x3 3. The attempt at a solution I circled the pivot element in row3,col3. It's a "1". I know I chose the pivot correctly(chose the most negative number in the bottom row, then found the column entry that is least when divided into the right-most column). Then I perform row operations to get all the rest of the numbers in the pivot column to be 0. Then I perform a row operation to turn the entry in the last row of the pivot column to 0. This makes the entire last row positive so the simplex algorithm is supposedly done--but it's not. The correct answer requires 200 deluxe sets and 100 basic sets be produced. I notice that I still have slack variables as basic variables. My guess is that I either performed the row operations incorrectly or there is some other step that I am overlooking. Ideas?