# Algebra

posted by .

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 -

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 -

32 + 100 = 132 at (4,10) wins

• Algebra -

Thank you Damon, your answer for this problem, and the other one was very thorough and easy to understand.

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