Share
Explore BrainMass

Answer to Statistics question: Quantitative Methods

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

Solution Summary

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

$2.19