erica is making necklaces and bracelets to se at the craft show. it takes her 3 hours to make a necklace and 2 hours to make a bracelet. she sells the necklaces for $18 and the bracelets for $15. she has 60 hours available this coming week to make the jewelry, and would like to make at least 25 total pieces of jewelry, with at least 2 being necklaces. how many of each should she make to maximize her profit?

Erica is making necklaces and bracelets to se at the craft show. it takes her 3 hours to make a necklace and 2 hours to make a bracelet. she sells the necklaces for $18 and the bracelets for $15. she has 60 hours available this coming week to make the jewelry, and would like to make at least 25 total pieces of jewelry, with at least 2 being necklaces. how many of each should she make to maximize her profit?

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Ranikashyab066Ace

Answer:

Erica should make at least 10 necklaces and 15 bracelets to maximize her profit of P = (18 x + 15 y)

Step-by-step explanation:

Let the number of necklaces made = x

Let the number of bracelets made by Erica = y

Now, the time taken to make each necklace = 3 hrs

⇒The time taken to make x necklaces = x times 3 hours = 3x

Also, the time taken to make each bracelet = 2 hrs

⇒The time taken to make y necklaces = y times 2 hours = 2y

So, total time taken to make x necklace and y bracelets = 3x + 2y

Now selling cost of 1 necklace = $18

Also, selling cost of 1 bracelet = $15

So, total selling price of x necklace and y bracelets = 18 x + 15 y

So according to the question:

x + y = 25 ..... (1)

3x + 2y = 60 .... (2)

Solving the above system substitute y = 25- x in (1)

we get: 3x + 2y = 60 ⇒ 3x + 2(25 -x) = 60

or, x = 10

⇒ y = 25 - x = 25 - 10 = 15, or y = 15

So, she should make at least 10 necklaces and 15 bracelets to maximize her profit of P = (18 x + 15 y)

Step-by-step explanation: