Chapter 4.2, Problem 28E

Set up and solve Exercises 23–29 by the simplex method.

28. Production 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. (See Exercise 30 in Section 4.1.)

1. (a) Assuming that all sets will be sold, bow many of each type should be made up in order to maximize profit? What is the maximum profit?
2. (b) A consultant for the Cut-Right Company notes that more profit is made on a Regular Set of knives than on a Basic Set, yet the result from part (a) recommends making up 100 Basic Sets but no Regular Sets. She is puzzled how this can be the best solution. How would you respond?