Set up Exercises 27–31 for solution by the simplex method. First express the linear constraints and objective function, then add slack variables to convert each constraint into a linear equation, and then set up the initial simplex tableau. The solutions of some of these problems will be completed in the exercises for the next section.

Business and Economics

30. Production—Knives 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 many of each type should be produced in order to maximize profit? What is the maximum profit?