A company sells sets of kitchen knives. A Basic Set consists of 5 utility knives

Question

A company sells sets of kitchen knives. A Basic Set consists of 5 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 $30 on a Basic Sets $50 on a Regular Set, and $60 on a Deluxe Set. The factory has on hand 1800 utility knives, 600 chef's knives, and 200 slicers. 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?

How many basic sets___

how many regular sets___

how many deluxe sets___

what is max profit__

Explanation / Answer

Let ' x ' be the basic set sold, " y ' be the regular set and ' z ' be the deluxe set sold

hence the following equations can be obtained

5 x + 2y + 3z = 1800

x + y + z = 600

y + z = 200 subject to the condition x > 0, y > 0 z >0 but the 3 equations doesnt obey this condition because

when we substittute y + z = 200 in the 2 nd equation we get x= 400 and if we put x = 400 in equation 1 we get

2y + 3 z = 1800 - 2000 = - 200 which violates the fact that all x , y , z ,are >0

please check the numbers

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