Posted by **Skyelar** on Monday, October 13, 2008 at 7:54pm.

I have just one more linear programming question, and then I think I'll be good. Thanks to everyone who answered my previous question, I am beginning to understand now.

Suppose you make and sell skin lotion. A quart of regualr skin lotion contains 2cups of oil, and one cup of cocoa butter. A quart of extra rich skin lotion contains 1 cup oil, and 2 cups of cocoa butter. You will make a profit of 10 per quart on regualar lotion, and a profit of $8 a quart on extra rich lotion. You have 24 cups oil, and 18 cups cocoa butter.

1. How many quarts of each type of lotion should you make to maximize your profit?

2. What is the maximum profit?

Thanks again

- Algebra -
**Damon**, Monday, October 13, 2008 at 8:53pm
r = regular (y axis)

e = extra rich (x axis)

p = profit = 8 e + 10 r

oil limit line (24 max)

oil = 2 r + 1 e, when e = 0, r limit is 12

when r = 0, e = 24

so oil line is

r = 12 - .5 e

butter limit line (18 max)

butter = 1 r + 2 e, when e = 0, r limit is 18

when r = 0, e limit is 9

so butter line is

r = 18 - 2 e

where is intersection of oil limit and butter limit lines?

4 r = 48 - 2 e

1 r = 18 = 2 e

-------------

3 r = 30

r =10

e = 4 so at (4,10)

so points

(0,0)

(0,12)

(4,10)

(9,0)

calculate profit = 8 e + 10 r at each point

- Algebra -
**Damon**, Monday, October 13, 2008 at 8:55pm
32 + 100 = 132 at (4,10) wins

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