 # You are a jeweler who sells necklaces and rings. Each necklace takes 4 ounces of gold and 2 diamonds myntfalskj4 2022-07-02 Answered
You are a jeweler who sells necklaces and rings. Each necklace takes 4 ounces of gold and 2 diamonds to produce, each ring takes 1 ounce of gold and 3 diamonds to produce. You have 80 ounces of gold and 90 diamonds. You make a profit of 60 dollars per necklace you sell and 30 dollars per ring you sell, and want to figure out how many necklaces and rings to produce to maximize your profits.

Clearly this is a maximization problem, and this is how I formulated it.

Let $n$, $r$, $g$, and $d$ represent units of necklaces, rings, gold, and diamonds, respectively.

Then, $n=4g+2d$, and $r=g+3d$.

Our profit can be defined by $p=60n+30r$.

Our constraints are $g\le 80$, and $d\le 90$.

I tried to approach solving this by substituting n and r for their production functions in the profit function. But, on second thought, I'm not sure if plugging them in maintains an equivalent profit function, because the gold/diamond amounts are tied together for each necklace/ring made.

So, I'm not sure if $p=60n+30r$ and $p=60\left(4g+2d\right)+30\left(g+3d\right)$ are equivalent statements.

Am I approaching this problem correctly? If not, how should I think about the problem? Thank you.
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it toriannucz
$d=3r+2n\le 90\phantom{\rule{0ex}{0ex}}g=1r+4n\le 80$
$P=30r+60n$
This then gives 3 allocations that maximize the use of resources.

All rings, All necklaces, and whatever combination is the solution to.
$3r+2n=90\phantom{\rule{0ex}{0ex}}1r+4n=80$
one of the 3 will be most profitable.

We have step-by-step solutions for your answer!