A company sells sets of kitchen knives. A Basic Set consists of2utility knives and 1 chef's knife. A Regular Set consists of2utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is

$30 on a Basic Set, $50 on a Regular Set, and $70 on a Deluxe Set. The factory has on hand 400 utility knives, 200 chef's knives, and 100 slicers

(a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit?

(b) A consultant for the company notes that more profit is made on a Regular Set than on a Basic Set, yet the result from part (a) recommends making up more Basic Sets than Regular Sets. She is puzzled how this can be the best solution. How would you respond?

(a) Find the objective function to be used to maximize profit. Let

x1 be the number of Basic Sets, let x2 be the number of Regular Sets, and let x3 be the number of Deluxe Sets.

What is the objective function

z=_ x1+_x2+_x3