Question

Lisa has an online jewelry shop where she sells earrings and necklaces. She sells earrings for $30 and necklaces for $40. It takes 30 minutes to make a pair of earrings and 1 hour to make a necklace, and, since Lisa is a math tutor, she only has 10 hours a week to make jewelry. In addition, she only has enough materials to make 15 total jewelry items per week. She makes a profit of $15 on each pair of earrings and $20 on each necklace. Calculate how many pairs of earrings and necklaces should Lisa make each week in order to maximize her profit, assuming she sells all her jewelry?

Answer 1

To maximize her profit, Lisa should calculate the number of earrings and necklaces she can make within her time and material constraints and then solve the system of inequalities and equations to determine the optimal number of each type of jewelry.

Step-by-step explanation:

In order to maximize her profit, Lisa should determine the number of pairs of earrings and necklaces she can make within her time and material constraints. Let's assume she makes x pairs of earrings and y necklaces in a week.

Given that it takes 30 minutes to make a pair of earrings and 1 hour to make a necklace, the total time used to make earrings and necklaces should be less than or equal to 10 hours: 0.5x + y <= 10.

Also, assuming she only has enough materials to make 15 total jewelry pieces, the total number of earrings and necklaces should be less than or equal to 15: x + y <= 15.

Finally, to maximize her profit, Lisa should calculate the total profit made from selling earrings and necklaces: 15x + 20y.

By solving the system of inequalities and equations, Lisa can determine the optimal number of earrings and necklaces she should make to maximize her profit.