Q2 The ETR obtained AD E Brokerage firms has just been instructed by one of its
ID: 1154534 • Letter: Q
Question
Q2 The ETR obtained AD E Brokerage firms has just been instructed by one of its clients to invest up to $250,000 for her money recently through the sale of land holdings in Toronto. The client has a good deal of trust in the investment use, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines: Municipal bonds should constitute at least 20% of the investment; At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers. No more than 50% of the amount invested in municipal bonds should be placed in a nursing home stock Subject to these constraints, the client goal is to maximize projected return on investments. The analysts at ETRADE Brokerage aware of these guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates of return Projected Rate of Return % 5.3 6.8 4.9 8.4 11.8 Investment Electronics Aerospace Drugs Nursing Homes a) Define the decision variables, (Ipt) b) Formulte the LP model of the given problem (objective function and the constraints) (3pts) c) Solve it by the MS Excel Solver (6pts)Explanation / Answer
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Answer to Question 2 part A: The ETRADE brokerage firm have been asked to invest upto $250000 on behalf of a client. Client has its preferences for the investment of the amount. There will be four types of decision variables as per the requirments of the client and they are as follows:
Answer to Part B:
total return(R) = type of instrument (i) X rate of return( rr) X amount Invested(A) X time period (t)
Total amount
250000
type of instrument
rate of return
Percentage of investment
investment
time
total return
municipal bonds
0.053
0.2
50000
1
2650
Electronic
0.068
0.2
50000
1
3400
Aerospace
0.049
0.25
62500
1
3062.5
drugs
0.084
0.1
25000
1
2100
nursing home
0.118
0.25
62500
1
7375
18587.5
So based on the LP model we can do investment as shown above, here we have assumed that allocation percentage and they are shown above and we have assumed that time is 1 year. Here we can see that total return is calculated $18587.5 if we spend the amount as shown above. We have assumed that amount invested in municipal bond, electronics, aerospace, drugs, nursing home is 20, 20, 25,10,25 % of total amount given for investment. And when we spend in this way we will get the return, which is mentioned above. This can change if we change the amount allocated for type of instrument. So all the variables are fixed except the amount allocation one. The variables such as time, rate of return are dependent variables and only independent variable here is amount of investment which means that if we change the amount of investment then change in total return can be there else it would same as shown above.
Answer to Part C:
Now lets solve the given problem by MS excel solver. MS excel solver is a way were various options are considered and best one is decided upon. MS excel solve checks upon different combination and then give sthe best and suited result. In our situation we will solve our problem of investment of given in such a way to maximize return and see wr the return is best and where allocated amount will give maximum result. We have tried to solve this situation in following manner through MS excel solver:
Total amount
250000
type of instrument
rate of return
Percentage of investment
investment
time
total return
municipal bonds
0.053
0.1
25000
1
1325
Electronic
0.068
0.1
25000
1
1700
Aerospace
0.049
0.1
25000
1
1225
drugs
0.084
0.1
25000
1
2100
nursing home
0.118
0.6
150000
1
17700
24050
So, here we see that by solving through MS excel solver the total return has changed as the amount allocated for investment has been changed and 60% of the total amount ahs been invested in Nursing home as its giving the highest rate of return and all the rest variables are given only 10% of the total amount. Here important thing to notice is that total return is a dependent variable because its totally dependent upon other variables such as time, rate of return, amount invested etc. Thus we see that MS excel solver maximizes our total return which is dependent variable here by considering four independent variables.
Total amount
250000
type of instrument
rate of return
Percentage of investment
investment
time
total return
municipal bonds
0.053
0.2
50000
1
2650
Electronic
0.068
0.2
50000
1
3400
Aerospace
0.049
0.25
62500
1
3062.5
drugs
0.084
0.1
25000
1
2100
nursing home
0.118
0.25
62500
1
7375
18587.5
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