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, $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?

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Author:WINSTON, Wayne L.
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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, $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?
Transcribed Image Text: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, $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?
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