Math Is Fun Forum

Hippo

Member

Registered: 2006-02-05

Posts: 2

Linear Programming?

Having alot of trouble figuring out this problem.  I feel if I can just see how its done I can complete the few other problems like this i have.  I wasnt in school for this portion of the chapter due to a surgery so im kind of in the dark on this whole process.  Anywho heres the problem:

you have decided to make a little extra money fro your club by selling candy.  You can buy M&m's and Snicker bars at cost from the Price Club, but there is a quantity limit.  Your book bag holds no more than 70 units of candy.  You can bring no more than 50 Snickers on any one day and no more than 30 M&M's on any one day.  Snickers cost you 30 cents each and M&ms cost you 25 cents each.  You sell them each fro 50 cents.  How can you maximize your profit?

Constraints:
1
2
3
4
5

Vertices:
1
2
3
4
5

C=
Max Score:

# of Snickers:
# of M&M's:

Whole problem made me a little hungry.  Any help/awnsers are appreciated.  Thanks in advance.

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darthradius

Member

Registered: 2005-11-28

Posts: 97

Re: Linear Programming?

Here's what I've got:

Max:  .2s + .25m     (OBJECTIVE FUNCTION)

subject to: (CONSTRAINTS)

s + m ≤ 70
s ≤ 50
m ≤ 30
s,m ≥ 0

Then, it sounds like you are using the Corner Point Theorem (I am assuming, since you asked for vertices).  So you would just graph the above constraints to find the feasible region, and then evaluate the objective function at each of the corner points:

Corner points (Vertices):
a = (0,0)
b = (50,0)
c = (0,30)
d = (40,30)
e = (50,20)

So evaluating your objective function at all of these points yields a maximum profit at corner point d=(40,30):

Max (C?) = $15.50 per day
with Snickers=40 and M&Ms=30

I hope that made sense....let me know if anything is unclear.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
                                                             -Bertrand Russell

Hippo

Member

Registered: 2006-02-05

Posts: 2

Re: Linear Programming?

Thank you, I appreciate your thorough response, after studying this for a few minutes I just tackled another problem and now feel comfortable with this.  Again, thank you!

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