Expert: Sherry Wallin - 9/28/2009

Question
I have asked a few experts so far, no one has been able to help.  Hoping to have more luck with you. If not, thanks anyway.

The Cut-Right Company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef’s knife. The Regular Set consists of 2 utility knives, 1 chef’s knife, and 1 slicer. The Deluxe Set consists of 3 utility knives, 1 chef’s knife, and 1 slicer. Their profit is $30 on a Basic Set, $40 on a Regular Set, and $60 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef’s knives, and 200 slicers. Assuming that all sets will be sold, how many of each type should be produced in order to maximize profit? What is the maximum profit?

Answer
John~
    I can help you out a bit but bear in mind that I haven't studied this in over 20 years...
You have certain constraints you need to consider:
Let w1 = the number of utility knives  -> 0<=w1<=800
Let w2 = number of chef knives  -> 0<=w2<=400
Let w3 = number of slicers  -> 0<=w3<=200
Now let x = # of basic sets      x = 2w1 + w2
   let y = # of regular sets    y = 2w1 + w2 + w3
   Let z = # of deluxe sets     z = 3w1 + w2 + w3
Your Profit equation is to maximize 30x + 40y + 60z
I hope this helps.
Math Prof