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Back Again - QM for Cobb-Douglas and Markowitz

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adodson Back Again - QM for... 03-26-2015, 10:34 PM
Alf Re: Back Again - QM for... 03-28-2015, 12:58 PM
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    Back Again - QM for Cobb-Douglas and Markowitz

    Hey guys,

    Was doing fine in this class but attempting to use the solver for the economic/investment type problems has thrown me through a loop. I've posted the two questinos below.

    The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form
    f (L, C) = c0Lc1Cc2
    Where c0, c1, and c2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital.
    a. In this example, assume c0 = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $75,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output.
    b. Find the optimal solution to the model you formulated in part (a). Hint: When using Excel Solver, start with an initial L > 0 and C > 0.

    The second is attached in the spreadsheet (Question 2). It is to formulate and solve the Markowitz portfolio optimization model using the data set included on the page.

    Any tips/points or help getting organized would GREATLY be appreciated.

    Question 1 - I tried to use S(L,C) as the objective function, L and C as the decision variables, and then Total Costs as the constraints and a few other variations to no avail. I do know the optimal value is 3750.

    Question 2 - I'm a little lost as what to use as the decision variables, maybe each years return based on the 6 funds? The teacher has some notes and I know the constraints are correct (10 is for 10% as the minimum return) and the second is the checksum of the percentage of each fund.

    Please let me know if some more information/explanation is needed.

    And thank you all for this forum!
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