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Math Help - Maximizing Sales

  1. #1
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    Maximizing Sales

    Hello All,
    I am having difficulty with this problem. I have managed to figure the constraints and objective formula (as seen below), but find myself needing assistance the rest of the way.

    Here is the Problem...

    A trucker carries cases of Pepsi and Coke into a region. His truck has the capacity to carry 1000 cases total. He must carry at least 200 cases of Pepsi, but no more than 400 cases of Coke. Each case of Pepsi is charged an import fee of $5 and each case of Coke is charged $10. The driver has a budget of $6000 to spend on import fees. If a case of Pepsi sells for $20 and a case of Coke for $25, how many cases of each should the driver carry so that he maximizes his sales?

    What I've managed to put together...

    Constraints:

    Let X = Pepsi
    Let Y = Coke

    X + Y ≤ 1,000

    5X + 10Y ≤ 6,000

    X ≥ 200

    Y ≤ 400

    Objective Formula:

    20X + 25Y
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  2. #2
    MHF Contributor
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    Re: Maximizing Sales

    You are missing the constraint \displaystyle \begin{align*} Y \geq 0  \end{align*} .

    Now graph these constraint inequalities to discover your feasible region, evaluate the co-ordinates of each corner point, and substitute each of these corner points into the objective function to find which gives the maximum sales and what the value of the maximum sales is.
    Thanks from seananigans
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