Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion MATH 105: Finite Mathematics 3-3: Linear Programming Story Problems Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006
Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion Outline Investment Allocation 1 Widget Production 2 Hotel Occupancy 3 Cruise Ships 4 Conclusion 5
Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion Outline Investment Allocation 1 Widget Production 2 Hotel Occupancy 3 Cruise Ships 4 Conclusion 5
Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion Investments: Problem Set-up Example An investment broker wants to invest up to $20,000. She can purchase type A bonds yielding a 10% return and she can purchase a more risky type B bounds yielding a 15% return. She wants to invest at least as much in the type A bond as in the type B bond to reduce her risk. The minimum investment for the type A bond is $5,000, and there are only $8,000 worth of type B bonds available. How much should the broker invest in each type of bond to maximize her returns?
Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion Investments: Problem Set-up Example An investment broker wants to invest up to $20,000. She can purchase type A bonds yielding a 10% return and she can purchase a more risky type B bounds yielding a 15% return. She wants to invest at least as much in the type A bond as in the type B bond to reduce her risk. The minimum investment for the type A bond is $5,000, and there are only $8,000 worth of type B bonds available. How much should the broker invest in each type of bond to maximize her returns? Constraints: Let: x be amount invested in A + 20 , 000 x y ≤ y the amount invested in B x ≥ y 5 , 000 x ≥ Objective: 8 , 000 y ≤ Maximize 0 . 10 x + 0 . 15 y 0 y ≥
Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion Investments: Locating Corner Points Example Continued. . . The region obtained from the constraints is shown below.
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