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
    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    how do you solve this problem? 1/2x - 3 = -1 Let me make sure I understand the problem. Do you mean (1/2)x - 3 = -1, i.e. .5x-3 = -1?
  2. Math - Reposted - Mahi's question

    Fill the seven quart. Empty into the five quart, leaving two. Mark the 7 quart jar at that 2 quart level. dump the five quart contents. Pour the 2 quarts into the five, marking its level. Fill the seven quart to the 2 quart level where …
  3. algebra

    thank everyone that site helped but now i just have to practice. for now can someone tell me how does 3x=7-4x x=1 which one do you minus or subtract from the equation?
  4. Algebra 2 Linear Programming

    I think this is an easy question but i just wanted make sure i have the right answer Could you check my work Some students make and sell jewelry in their spare time. Every week they have an avaiable 10,000 beads of various colors and …
  5. English Essay Writing

    I posted my English essay homework on March 17,2008 and no one has answered my question yet. I understand that every question may not be answered but I was just wondering If anyone that was good at Eassy writing could take a look thanks …
  6. chemistry

    Good day to everyone My class has just started a "Chemistry systems in Equilibrium" unit and I have a question I would like answered if possible, I would truly appreciate this. My Question: How will the following system change when …
  7. Algebra

    Thanks for those who answered my previous question! I have just one more: x^2-625=0, what is the GCF?
  8. English

    Thank you. I think i have it now, just one more question can an introduction be two sentences or does it have to be five or more. thank you for your patients
  9. Linear Algebra - Question

    I have this number that I just wanted to be sure how to do. They give me a Parallelepiped with corners lettered from A to H. Then the question is: In a certain orthonormal reference, the coordinates of points A, B, D and E are respectively …
  10. English

    Let's review the previous lesson. What did we learn last time?

More Similar Questions