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Function with calculates the profit in terms of qty sold!

  1. Oct 30, 2009 #1
    1. The problem statement, all variables and given/known data
    A speciality coffee shop sells Cuban coffee beans for $5.50 each bag and Colombian coffee beans for $3.80 a package.
    1.If the cost of sales is $1450 plus $0.95 per bag, write down the function which calculates the profit in terms of the number of bags of coffee beans sold.
    2. If they sell 225 bags of Cuban , how much Colombian coffee must be sold in order to break even?
    3. If they require a profit of $1200, and they sell 500 bags of Cuban, how much Colombian must be sold?
    4. Suppose the demand for Colombian is six times the demand for Cuban. How much Cuban coffee must be sold to make a profit of $2300?



    3. The attempt at a solution
    Here is what I've attempted, how ever I am really confused...
    P(x1,x2) = -1450 + 0.95x1+0.95x2
    P(225,x2) = -1450 + 0.95(225) +0.95x2
    -1450 +213.75+0.95x2
    =-1236.75+0.95x2
    0.95x2=1236.75
    x2=1236.75/.95
    x2 = 1301

    Is this correct, or what is missing?
    Please help!!!
     
  2. jcsd
  3. Oct 31, 2009 #2

    Mark44

    Staff: Mentor

    What do x1 and x2 represent? That should be the first thing you say.

    What your formula says is that they make $.95 for each bag that goes out the store, and that they have to pay out $1450. That's wrong. It costs them $.95 for each bag they use.

    You would think that the $5.50 per bag of Cuban coffee and $3.50 per bag of Colombian coffee would enter into their profit function somehow.

    Do you understand the concept of profit? profit = revenue - costs.
     
  4. Oct 31, 2009 #3
    Hello Mark,

    Thank's for replying.

    Here is my new attempt:
    LET x1 =represent the number of Cuban coffee sold
    LET x2 =represent the number of Colombian coffee sold

    R(X) = $5.50x1 + $3.80x2
    C(x) = $1450 + 0.95x1 + 0.95x2
    P(x) = R(X) - C(X)
    P(X) = 5.50x1 + 3.80x2 -1450 - 0.95x1 -0.95x2
    P(X) = 4.55x1 +2.85x2-1450

    Is this correct now?
    Please let me know

    Thank you
     
  5. Oct 31, 2009 #4

    Mark44

    Staff: Mentor

    Yes, that's right. For the sake of clarity, x1 and x2 represent the number of bags of each kind of coffee.

    Now that you have the first part, can you do the next three parts? It will be easier now that you know what your variable represent.
     
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