Answer:
10 pairs of earrings and 5 necklaces (the maximum profit will be $250)
Step-by-step explanation:
Let x be the number of earrings and y be the number of necklaces Lisa makes.
1. Lisa only has enough materials to make 15 total jewelry items per week, then
[tex]x+y\le 15.[/tex]
2. It takes half an hour to make a pair of earrings, so it takes her [tex]\dfrac{1}{2}x[/tex] hours to make x earrings. It takes her 1 hour to make a necklace, so it takes her y hours to make y necklaces. Lisa only has 10 hours a week to make jewelry, thus
[tex]\dfrac{x}{2}+y\le 10[/tex]
3. Lisa makes a profit of $15 on each pair of earrings and $20 on each necklace. In total her profit is
[tex]P=15x+20y.[/tex]
You have to find the maximum value of the function [tex]P=15x+20y[/tex] with respect to inequalities
[tex]x+y\le 15\\ \\\dfrac{x}{2}+y\le 10[/tex]
Draw the solution set on the coordinate plane (see attached diagram). The maximum value of the efunction P is at point (10,5) and is
[tex]P=15\cdot 10+20\cdot 5=150+100=\$250[/tex]
