SOLUTION: A jewelry craftsman produces bracelets and necklaces that contain both gold and platinum. The following table shows the amounts of precious metals used in the production of thes
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Question 532203: A jewelry craftsman produces bracelets and necklaces that contain both gold and platinum. The following table shows the amounts of precious metals used in the production of these items.
Metal Content (grams) Grams Available
Bracelet Necklace per week
Gold 12 6 120
Platinum 9 18 144
Suppose the craftsman makes a profit of $130 on each bracelet and $90 on each necklace. Calculate the craftsman’s maximum weekly profit and how many of each item he should produce each week.
I just answered a Linear Programming problem, probably for you, but in any case you can look it up for yourself.
Presuming represents the number of bracelets and represents the number of necklaces:
Your profit function that you want to maximize is:
Subject to:
The integer constraint is required because you can't make and sell fractional parts of bracelets or necklaces -- can you imagine trying to wear 45.3% of a bracelet? I put this in as a general consideration -- something for you to think about any time you work a Linear Programming problem. However, the issue is moot for this particular problem since you will find, once you graph your constraint inequalities, that all four vertices of your feasibility quadrilateral have integer coefficients.
Follow the instructions in the other problem (# 532189) and the information above to solve this. Or write back and we can negotiate a price for a full graphical or Excel spreadsheet based solution.
John
My calculator said it, I believe it, that settles it
