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    Linear Programming Model for Maximization

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    [IV](20) The Golden Gate Cranberry Company purchases cranberries from local growers and
    makes cranberry sauce and cranberry juice. It costs $0.70 to produce a can of cranberry sauce
    and $0.95 to produce a bottle of cranberry juice. In order to present a representative marketing mix
    to its customers the company has made it a policy that at least thirty percent, but not more than
    sixty percent, of the items it produces be cranberry sauce.
    The company wants to produce up to, but no more than, the demand for each product. The
    company marketing manager estimates that the demand for cranberry sauce is a maximum of
    5,000 cans plus an additional 3 cans for each $1 spent on advertising. The maximum demand
    for cranberry juice is estimated to be 4,000 bottles plus an additional 5 bottles for every $1 spent
    to promote cranberry juice. The company has $16,000 to spend on producing and advertising
    cranberry sauce and cranberry juice. Cranberry sauce sells for $1.45 per can while cranberry juice
    sells for $1.75 per bottle.
    The company wants to know how many units of each cranberry product to produce and how
    much to spend on advertising for each product in order to maximize profit. Formulate a linear
    programming model for this problem. Make sure you clearly define decision variables. Do not
    attempt to solve this problem.

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    https://brainmass.com/math/linear-programming/linear-programming-model-maximization-350265

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    Decision Variables:
    x = The number of cans of sauce produced
    y = The number of bottles of juice produced
    z = Amount in dollars spent on advertising
    Objective Function:
    Maximize Profit, P = 1.45x + 1.75y
    Constraints:
    0.70x + 0.95y + z ≤ 16000 [Cost]
    0.3(x + y) ≤ x ≤ 0.6(x + y), that is (a) -0.7x + 0.3y ≤ 0 and (b) 0.4x - 0.6y ≤ 0 [Representative Mix]
    x ≤ 5000 + 3z, that is x - 3z ≤ 5000 [Demand for Sauce]
    y ≤ 4000 + 5z, that is y - 5z ≤ 4000 [Demand for Juice]
    x, y ≥ 0 and Integers, and z ≥ 0 [Non-negativity]

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:10 pm ad1c9bdddf>
    https://brainmass.com/math/linear-programming/linear-programming-model-maximization-350265

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