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, $50 on a Regular​ Set, and $70 on a Deluxe Set. The factory has on hand 1200 utility​ knives, 600 chef's knives, and 300 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) To maximize​ profit, the company should make up ____Basic​ Sets, ____Regular​ Sets, and ___Deluxe Sets.

​(Simplify your​ answers.)

The maximum profit is ​$_______.

​(Simplify your​ answer.)

​(b) Choose the correct answer below.

A. 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.

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

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

Answer 1

utility no. of profit knives chef knife slicer profit sets sold derived basic set 0 40 150 6000 regular set 50 0 deluxe set 70 300 21000 total required 1200 450 300 maximum total available 1200 600 300 profit 27000 we used solver to find the maximum profit where red colour cell is the objective pink depicts changing variables blue colour cells are subject and green cells are contraints 12 14 15 the profit is maximized by selling 150 basic sets O regular sets 300 deluxe sets maximum profit is $27000 since regular set requires slicer but due to limited quantity of slicers availabe regular sets are set to 0 and all the slicers are used in deluxe set due to more profit generation on deluxe set. therefore, even because of less profit on basic set, basic sets are sold over regular sets 26 B. 27 the corret answer is option A the major proportion of profit is shared by deluxue set of $21000