How may I help you, Justine? Justine makes jewelry. She can currently make a pair of earrings with 20 beads in 30 minutes and a necklace with 30 beads in 30 minutes. She plans to use no more than 600 beads, work a maximum of 12 hours (720 minutes) and make at least 5 pairs of earrings and 5 necklaces. She makes $3.25 profit on each pair of earrings and $5.00 profit on each necklace. How many of each should she make to maximize a profit?

What can we pull out of your question? Justine makes jewelry. She can currently make a pair of earrings with 20 beads in 30 minutes and a necklace with 30 beads in 30 minutes. She plans to use no more than 600 beads, work a maximum of 12 hours (720 minutes) and make at least 5 pairs of earrings and 5 necklaces. She makes $3.25 profit on each pair of earrings and $5.00 profit on each necklace. How many of each should she make to maximize a profit?

Now, What does each color mean? Blue = Variables Pink = Bead Values Green = Minute Values Red & Purple = Minimal Production Values Yellow = Profit Values

How can we use these values? Our Formulas: E > 5 You must make at least 5 pairs of earrings N > 5 You must make at least 5 necklaces 20E + 30N < 600 You use 20 beads per each pair of earrings and 30 beads per each necklace, with a maximum of 600 beads 30E + 30N < 720 You spend 30 minutes on each pair of earrings and 30 minutes on each necklace, with a maximum of 720 minutes

Earrings

Let me do the math... Point A E = 5 N = 5

Point B 20E + 30N = (E = 5) 30N = 500 N = 16 2/3 E = 5

Point C -1 (20E + 30N = 600) + 30E + 30N = E = 120 E = 12 20(12) + 30N = N = N = 360 N = 12

Point D 30E + 30N = (N = 5) 30E = 570 E = 19 N = 5

Your Profits! P = 3.25E + 5N A 3.25(5) + 5(5) = B 3.25(5) + 5(16 2/3) = C 3.25(12) + 5(12) = D 3.25(19) + 5(5) = 86.75

Profit Statement To Maximize profit by $99.58, make 5 pairs of earrings and 16 2/3 necklaces.