Maximizing Profit at a Jewelry Store

What profit for a necklace would result in no bracelets being produced, and what would be the optimal solution for this profit?

The profit for a necklace would need to be greater than the profit for a bracelet in order for no bracelets to be produced. What would be the optimal solution for this profit?

Answer:

If the profit for a necklace were $500, for example, the store would choose to produce only necklaces in order to maximize profit. The optimal solution for this profit would be to produce as many necklaces as possible using the available gold and platinum.

To calculate the profit for a necklace that would result in no bracelets being produced, we need to compare the profits for both necklaces and bracelets. Since a necklace earns $300 in profit and a bracelet earns $400, the profit for a necklace would need to be greater than $400 for no bracelets to be produced.

In this scenario, we can set the profit for a necklace at $500. With this profit margin, the store would prioritize producing necklaces over bracelets as they would generate more profit per item. By producing as many necklaces as possible, the store can maximize its profit.

For the given data, each necklace requires 3 ounces of gold and 2 ounces of platinum, while each bracelet requires 2 ounces of gold and 4 ounces of platinum. The available resources are 18 ounces of gold and 20 ounces of platinum. With a profit of $500 for each necklace, the store can produce 6 necklaces, utilizing all 18 ounces of gold and 12 ounces of platinum.

As a result, no bracelets would be produced in this scenario, and the total profit would amount to $3000 from the 6 necklaces. This optimal solution allows the store to make the most of its resources and generate the highest profit possible.