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)
