QUESTION 3: As a 401K retirement plan participant you have to make personal deci
ID: 2731956 • Letter: Q
Question
QUESTION 3:
As a 401K retirement plan participant you have to make personal decisions regarding your own investment objectives. Suppose you have $10,000 to divide among four investment alternatives in your 401K retirement plan. The investment alternatives and historical returns are as follows;
Real Estate (RE) = 8%
CD = 4%
Mutual Fund (MF) = 6%
Bonds = 7%
You will follow the investment allocation guidelines below.
More money should be in real estate than in CDs, at a rate of at least 2 to 1.[Hint:That means that RE > 2*CD]
At least 50% ($5,000) must be in mutual funds and bonds combined.
No more than 20% ($2,000) can be in bonds alone.
At least 2.5% ($250) must be invested in each alternative.
All of the $10,000 must be invested.
Use the spreadsheet template in the worksheet named “Investment 1” to formulate and solve the LP problem for the maximum return. Note that the percentages must be expressed as proportions in the solution.
Answer the parts below, and then use the LP template to solve for the maximum profit. (4 points) Be sure to choose “assume Linear Model” and “Assume Non-negative” from Solver’s Options dialogue box.
2 Points: In cell B3, use the Excel’s built-in function named “SUMPRODUCT” to write a formula for the objective function.Be sure to reference the appropriate cells.
2 Points: In cells B9:E9, enter the investment return coefficients for the objective function.Make sure the coefficients are input as proportions, not percents.
8 Points: In cells B12:E19, enter the constraint coefficients for each of the eight constraints.
4 Points: In cells F12:F19, enter the appropriate constraint values.
8 Points: In cells G12:G19, use the “SUMPRODUCT” function to write a formula for the amount of each resource used or limitation imposed.Be sure to reference the appropriate cells.
4 Points: In cells H12:H19, write the appropriate formulas to determine the amount of slack or surplus associated with each resource or limitation.
4 Points: In cells I12:I19, write the type of inequality associated with each constraint using either “<=,” “>=,” or “=.”
4 Points: In cells J12:J18, write the appropriate word (either “Slack” or “Surplus”) to indicate the nature of the leftover resources or limitations.
Question 3 Part a Grader Max Return X1 RE X2 CD X3 MF X4 Bonds Grader Dec Vars Part b X1 RE X2 CD X3 MF X4 Bonds Grader Return Coefficients Part c Part d Part e Part f Part g Part h Constraint Coefficients X1 RE X2 CD X3 MF X4 Bonds Constraint Value Amount Used Slack or Surplus Type Inequality Slack or Surplus RE to CD Ratio MF + Bonds Combined Bonds <=$2000 RE Alone CD Alone MF Alone B Alone All Funds Invested Grader Grader Grader Grader Grader GraderExplanation / Answer
Part a
Grader
Max Return
0.08X+0.04X+0.06X+0.07X
X1 RE
X2 CD
X3 MF
X4 Bonds
Grader
Dec Vars
Assume linear model
Assume linear model
Assume linear model
Assume linear model
Part b
X1 RE
X2 CD
X3 MF
X4 Bonds
Grader
Return Coefficients
0.08
0.04
0.06
0.07
Part c
Part d
Part e
Part f
Part g
Part h
Constraint Coefficients
X1 RE
X2 CD
X3 MF
X4 Bonds
Constraint Value
Amount Used
Slack or Surplus
Type Inequality
Slack or Surplus
RE to CD Ratio
-1
2
0
0
<
0
2X-X+S
<
Slack
MF + Bonds Combined
0
0
1
1
>
5000
X+X-S+A
>
Surplus
Bonds <=$2000
0
0
0
1
<
2000
X+S
<
Slack
RE Alone
1
0
0
0
>
0
Non Negative assumptions
>
Surplus
CD Alone
0
1
0
0
>
0
Non Negative assumptions
>
Surplus
MF Alone
0
0
1
0
>
0
Non Negative assumptions
>
Surplus
B Alone
0
0
0
1
>
0
Non Negative assumptions
>
Surplus
All Funds Invested
1
1
1
1
<
10000
X+X+X+X+S
<
Slack
Part a
Grader
Max Return
0.08X+0.04X+0.06X+0.07X
X1 RE
X2 CD
X3 MF
X4 Bonds
Grader
Dec Vars
Assume linear model
Assume linear model
Assume linear model
Assume linear model
Part b
X1 RE
X2 CD
X3 MF
X4 Bonds
Grader
Return Coefficients
0.08
0.04
0.06
0.07
Part c
Part d
Part e
Part f
Part g
Part h
Constraint Coefficients
X1 RE
X2 CD
X3 MF
X4 Bonds
Constraint Value
Amount Used
Slack or Surplus
Type Inequality
Slack or Surplus
RE to CD Ratio
-1
2
0
0
<
0
2X-X+S
<
Slack
MF + Bonds Combined
0
0
1
1
>
5000
X+X-S+A
>
Surplus
Bonds <=$2000
0
0
0
1
<
2000
X+S
<
Slack
RE Alone
1
0
0
0
>
0
Non Negative assumptions
>
Surplus
CD Alone
0
1
0
0
>
0
Non Negative assumptions
>
Surplus
MF Alone
0
0
1
0
>
0
Non Negative assumptions
>
Surplus
B Alone
0
0
0
1
>
0
Non Negative assumptions
>
Surplus
All Funds Invested
1
1
1
1
<
10000
X+X+X+X+S
<
Slack
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