# 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

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#### Solution Summary

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