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A company sells sets of kitchen knives. A basic set consists of2 utility knives and 1 chef's knife. A regular set consists of 2utility knives, 1 chef's knife, and 1 slicer. A deluxe set consistsof 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, and400 slicers.

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

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

(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 ofRegular 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 ____ BasicSets, ____ 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 canbe made up than Regular Sets. This results in higher overallprofit.

B.The Basic Set requires fewer knives.​ So, fewer Basic Sets canbe made up than Regular Sets. This results in higher overallprofit.

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

D.The overall profit is most affected by the Deluxe Set. Theprofit generated by the Basic Set and Regular Set does notsignificantly contribute to the overall profit.