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 ​$20 on a Basic​ Set, ​$60 on a Regular​ Set, and ​$70 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 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

​(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, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit.

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

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

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

A company sells sets of kitchen knives. A Basic Set consists of 2 utility knives and 1 chefs knife. A Regular Set consists of 2 utility knives, 1 chefs knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chefs knife, and 1 slicer. The profit is $20 on a Basic Set, $60 on a 1600 utility knives, 800 chefs 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 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? hand Regular Set, and $70 on a Deluxe Set. The factory has on 1 profit is made on a Basic Set, yet the result Regular Set than on a $20 $60 $70 Basic Sets Regular Sets Deluxe Sets Utility knives Chefs knife <1600 2 2 3 1 1 1 800 <400 Slicer 0 1 1 (a) Find the objective function to be used to maximize profit. Ans. 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? Ans.

Maximize z 20x +60x+70x Subject to: 2x 2x+3x3 1600 x800 +x400 0 B F A C E 1 $60 $70 $20 2 Basic Sets Regular S Deluxe Sets 3 Max. Profit Capacity 32,000 4 400 Decision variables 200 5 Constraints 6 Utlity knives 2 2 3 1600 1600 7 Chefs knife 600 800 1 1 1 8 Slicer 0 1 400 400 9 To maximize profit, the company should make up 200 Basic Sets, 0 Regular Sets, and 400 Deluxe Sets The maximum profit is $32,000. (b) Choose the correct answer below Ans. A. The Basic Set requires fewer knives. So, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit. rt LO