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# Linear Programming : Optimization and Maximization

Joe has \$250,000 to invest.
He is considering four options"
Bonds Fund Exxon MicroSoft Real Estate Fund
Price per share \$50 \$100 \$80 \$40
Annual Rate of Return 0.06 0.12 0.08 0.09
Risk measure per \$ invested 0.05 0.10 0.08 0.11

Joe wants at least a 9% annual rate of return
No one stock can be more than 50% of the total dollar investment
What investment would minimize the risk?
What would be the return?

Problem 10
Elko makes three bicycles requiring operations in fabrication, painting, and assembly

Operation Time Requirement
Operation Boys Girls Toddlers
Fabrication 1 1.1 0.9
Painting 0.5 0.6 0.4
Assembly 0.3 0.3 0.4

For the next month, the labor hours available are 300 in fabrication, 250 in painting and 180 in assembly.
Profits are #30 for a boys bike, \$28 for a girls, and \$25 for a toddlers
Setup costs are \$525 for boys bikes, \$600 for girsl, and \$450 for toddlers
What is the maximum net profit after taking setup costs into consideration and how many bikes of each type will be made?

Note we will make no more than 200 boys bikes, no more than 160 girls bikes, and no more than 125 toddlers.

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Problem 9

Joe has \$250,000 to invest.
He is considering four options"
Bonds Fund Exxon MicroSoft Real Estate Fund
Price per share \$50 \$100 \$80 \$40
Annual Rate of Return 0.06 0.12 0.08 0.09
Risk measure per \$ ...

#### Solution Summary

Linear programming optimization and maximization is discussed. The investments to minimize the risks are determined.

\$2.19