Question

A company sells sets of kitchen knives. A basic set consists of 2 utility knives and 1 chef's knife. A regular set consists of 2 utility 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 $40 on a Basic Set, $60 on a regular set, and $80 on a Deluxe Set. The factory has on hand 1600 utility knives, 800 chef's knives, and 400 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 x_(1) be the number of Basic Sets, let x_(2) be the number of Regular Sets, and let x_(3) be the number of Deluxe Sets.

What is the objective function?

z=___ x_(1) + ___ x_(2)+___ x_(3)

(a) To maximize profit, the company should make up ____ Basic Sets, ____ Regular Sets, and ____ Deluxe Sets.

The maximum profit is $____.

(b) Choose the correct answer below,

A. The Basic Set requires fewer knives.​ So, more Basic Sets can be made up than Regular Sets. This results in higher overall profit.

B.The Basic Set requires fewer knives.​ So, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit.

C.Since the Regular Set requires more​ knives, it has higher production costs. This will result in less profit than the Basic Set.

D.The overall profit is most affected by the Deluxe Set. The profit generated by the Basic Set and Regular Set does not significantly contribute to the overall profit.

Answer 1