Expert: Chanda Walker - 3/15/2009

Question
A local herb shop is producing two natural perfumes: Gentle Rose and Rich Gardenia. The owner, who has equipment that can make up to 3000 ounces of perfume, cannot afford to spend more than $9000. The Gentle Rose is 2 ounces large and costs $3 to make with a profit over cost of 4$. The Rich Gardenia is 1.5 ounces big and cost $6 with a profit over cost of 5$. How many bottles of each perfume should be made for max profit and what is the max profit?

Answer
P = GR * $4 + RG * $5
C = GR * $3 + RG * $6 <= $9000
V = GR*2 + RG*1.5 <= 3000



Solving the inequalities for GR

GR <= 3000 - 2RG
GR <= 1500 - 3/4 RG

Setting this equal.

3000 - 2RG = 1500 - 3/4 RG
1500 = 5/4 RG
RG = 1200

GR = 600

This will generate a cost of $9000, a volume of 3000, and a profit of $8400.

Let me know if I can help further.