Question 1117364: this is linear programming I am having hard time to understand each step :( pls help me I need to report this tomorrow it's a big help of yours. thank you very much!!!
After making various presentations to potential investors, MC has finally hit the jackpot. An investor wants to invest 100,000,000 pesos in MC.
After doing all your staff work in the previous weeks, the two of you have been tasked to find the most efficient way to invest the money. This involves making the highest profit possible from the money you have invested. You have decided to consult your friend Olivia, who is also a financial investor.
Olivia discusses that you need to use a mathematical method called Linear Programming to solve this problem. She explains that Linear Programming is a method that has to be set up very carefully. It involves creating a function to optimize and modelling various constraints using linear equations. She has decided to present you the profitability percentages of MC, given that she has already done prior work with MC.
The startup arm is projected to return at least 12%. To minimize risk, you must invest no more than 30,000,000 pesos. The financial stocks return 3%, while the retail arm returns 5%.
For tax reasons, you must invest at least 3 times more in the financial stocks than the retail arm.
Your task is to set up the linear program. You have to define the following:
The variables that will be used
The optimization function that will be used
What kind of optimization will be done: minimization or maximization?
The constraints that the linear program will be subjected to
The model will be presented to the MC CEO, who will verify if the model is satisfactory.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The startup arm is projected to return at least 12%.
To minimize risk, you must invest no more than 30,000,=000 pesos. The financial stocks return 3%, while the retail arm returns 5%.
f + r <= 30,000,000
Optimization:: Payoff = 0.03f + 0.05r
For tax reasons, you must invest at least 3 times more in the financial stocks than the retail arm.
f >= 3r
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Your task is to set up the linear program.
You have to define the following:
The variables that will be used:: f = amt. invested in financial stocks;
r = amt. invested in retail
The optimization function that will be used:: see above
What kind of optimization will be done: minimization or maximization?
Ans: maximization of Payoff
The constraints that the linear program will be subjected to
0<= f <= 30,000,000
0<= r <= 30,000,000
f <= -r+30,000,000
f >= 3r
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Procedure:: Graph these constraints in an r/f coordinate system
Find the coordinates of the intersection of the various pairs
of constraints.
Test those coordinate values in the Optimization statement to
find the r/f values that optimize the Payoff.
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Cheers,
Stan H.
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