invest a total of $50,000. Because of the risk, he will limit his investment in oil leases and stocks to 30% and his investment in oil leases and bonds to 50%. Assuming that inve Let o the amount invested in oil leases, Lets the amount invested in stocks, and Let b the amount invested in bonds Which option (a, b, c, or d) shows the correct objective function and constraints for this application? Objective Function: Maximize Return, R-15%6*o +996*s +596*b Constraints: o+s+b=50,000, o+s<= 30%6*50,000, o+b<= 50%6*50,000, o >= 0, Objective Function: Maximize Return, R=996*o +596*s +1596-b Constraints: o+s+b=50,000,o+s< 30 % 50,000, o+b< 50 % 50,000, o >= 0, O Objective Function: Maximize Return, R=1596*o +996*s +596*b Constraints: o+s+b<50,000,o+s<30% +50,000, o+b< 50 % +50,000, o>- 0, O Objective Function: Maximize Return, R=15%6*o +996 *s +596*b Constraints: o+s+b<50,000, o+s>= 30% +50,000, o+b>50% -50,000, >= 0, s>= 0, b <=0 s>= 0,6 <=0 s>= 0, b <= 0 s>= 0, b <= 0
invest a total of $50,000. Because of the risk, he will limit his investment in oil leases and stocks to 30% and his investment in oil leases and bonds to 50%. Assuming that inve Let o the amount invested in oil leases, Lets the amount invested in stocks, and Let b the amount invested in bonds Which option (a, b, c, or d) shows the correct objective function and constraints for this application? Objective Function: Maximize Return, R-15%6*o +996*s +596*b Constraints: o+s+b=50,000, o+s<= 30%6*50,000, o+b<= 50%6*50,000, o >= 0, Objective Function: Maximize Return, R=996*o +596*s +1596-b Constraints: o+s+b=50,000,o+s< 30 % 50,000, o+b< 50 % 50,000, o >= 0, O Objective Function: Maximize Return, R=1596*o +996*s +596*b Constraints: o+s+b<50,000,o+s<30% +50,000, o+b< 50 % +50,000, o>- 0, O Objective Function: Maximize Return, R=15%6*o +996 *s +596*b Constraints: o+s+b<50,000, o+s>= 30% +50,000, o+b>50% -50,000, >= 0, s>= 0, b <=0 s>= 0,6 <=0 s>= 0, b <= 0 s>= 0, b <= 0
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:Investments An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment into stocks with a potential return of 9%, and a relatively safe bond investment with a potential return of 5%. He plans to
invest a total of $50,000. Because of the risk, he will limit his investment in oil leases and stocks to 30% and his investment in oil leases and bonds to 50%. Assuming that investment returns are as expected, how much should be invested in each in order to maximize his return?
Let o = the amount invested in oil leases,
Let s = the amount invested in stocks, and
Let b = the amount invested in bonds
Which option (a, b, c, or d) shows the correct objective function and constraints for this application?
O Objective Function: Maximize Return, R = 15% *o +9%*s + 5%*b
Constraints: o + s + b = 50,000, o+s<= 30% *50,000, o + b <= 50%6*50,000, >= 0,
O Objective Function: Maximize Return, R = 99% *o + 5%*s + 15%*b
Constraints: o+s+ b = 50,000, o+s<= 30% *50,000, o + b <= 50%6*50,000, o >= 0,
O Objective Function: Maximize Return, R = 15%*o +9 %*s + 5%*b
Constraints: o + s + b < 50,000, o+s<= 30% *50,000, o + b <= 50%6*50,000, >= 0,
O Objective Function: Maximize Return, R = 15% *o + 9%*s + 5%*b
Constraints: o+s+b<50,000, o+s>= 30% *50,000, o + b >= 50% *50,000, o >= 0,
s>= 0, b <= 0
s>= 0, b <= 0
s>= 0, b <= 0
s>= 0, b <= 0
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Linear programming is an optimization technique that can be used when there are limited resources and unlimited wants that need to be met. This technique involves formulating an objective function and constraints which define a problem, finding its optimal solution, and then using those results to find other solutions that are near-optimal.
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