Explore BrainMass
Share

Explore BrainMass

    Answer to Statistics question: Quantitative Methods

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

    Joe is going to invest $250,000 in the development of new products. The new products have the following expected costs, yields, and degrees of risk.

    Expected Expected Expected
    Product Cost Yield Risk
    A $100,000 0.20 8
    B $50,000 0.10 4
    C $50,000 0.15 10
    D $150,000 0.10 0

    Joe can do each product at its full cost or he may attempt a partial development and still expect a yield proportional to the level of expenditure on the product. Joe wants to limit his total weighted risk(degree of risk times budgeted amount) to 1000000 units; that is, an adopted plan for a $10000 expenditure with a degree of risk of 7 would be 70000 riskunits.

    What should Joe invest to net the highest yield given his risk constraints?

    Answer:

    Decision Variable Product A Product B Product C Product D
    100000 50000 0 150000

    Objective function:
    Maximize the yield 20000 5000 0 15000
    Total Yield 40000

    Constraints
    Risk 800000 200000 0 0
    Total Risk 1000000
    Limit on Risk 1000000

    Limit on investment in each product
    Available 100000 50000 50000 150000
    Used 100000 50000 0 150000

    Run solver to solve the LP
    See the solver output. Thus, the following investments should be made in four products
    A 100000
    B 50000
    C 0
    D 150000

    Decision Variable Product A Product B Product C Product D
    100000 50000 0 150000

    Objective function:
    Maximize the yield 20000 5000 0 15000
    Total Yield 40000

    Constraints
    Risk 800000 200000 0 0
    Total Risk 1000000
    Limit on Risk 1000000

    Limit on investment in each product
    Available 100000 50000 50000 150000
    Used 100000 50000 0 150000

    The following investments should be made in 4 products:
    A 0
    B 0
    C 0
    D 0

    This is an investment problem in linear programming. Please solve and show work

    © BrainMass Inc. brainmass.com October 9, 2019, 7:32 pm ad1c9bdddf
    https://brainmass.com/statistics/quantative-analysis-of-data/answer-to-statistics-question-quantitative-methods-121069

    Solution Summary

    Word document contains complete formulation and explanation. The excel file contains formulation in Solver tool dialogue box and optimal solution.

    $2.19