Set up for solution by the simplex method.
First express the linear constraints and objective function, then
add slack variables, 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.
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?