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Please help me with problem 2 and 11 (Introduction to Management science course)

src="/qa/attachment/10702244/" alt="Screenshot (3).png" />Chapter 8 Problem 11.png

Chapter 8 Problem 11.png

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Problems
401
b. Use LINGO or Excel Solver to find the solution to your mathematical model to deter-
mine the optimal number of gloves to produce at each facility.
est
11. In the Markowitz portfolio optimization model defined in equations (8.10) through (8.19),
the decision variables represent the percentage of the portfolio invested in each of the
mutual funds. For example, FS = 0.25 in the solution means that 25% of the money in
the portfolio is invested in the foreign stock mutual fund. It is possible to define the deci-
sion variables to represent the actual dollar amount invested in each mutual fund or stock.
Redefine the decision variables so that now each variable represents the dollar amount
invested in the mutual fund. Assume an investor has $50,000 to invest and wants to mini-
mize the variance of his or her portfolio subject to a constraint that the portfolio returns a
minimum of 10%. Reformulate the model given by (8.10) through (8.19) based on the new
definition of the decision variables. Solve the revised model with LINGO or Excel Solver.
12. Many forecasting models use parameters that are estimated using nonlinear optimization.
A good example is the Bass model introduced in this chapter. Another example is the ex-
ponential smoothing forecasting model. The exponential smoothing model is common in
logi
If..4har detail in Chanter 15. For instance. the basic exponential
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6:26 PM
10/2/2019

Screenshot (3).png

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excise is to provide practice using LINGO or Excel Solver. Find the
values of X and Y that minimize the function
Min X2 - 4X + Y2 + 8Y + 20
Do not assume nonnegativity of the X and Y variables. Recall that by default LINGO assumes
nonnegative variables, In order to allow the variables to take on negative values you can add
@FREE(X); @FREE(Y):
Alternatively, if you want LINGO to allow for negative values by default, in the LINGO
menu select Options and then click General Solver, and then uncheck the Variables
assumed nonnegative tab. To allow for negative values in Excel Solver, make sure that
the Make Unconstrained Variables Non-Negative box is not checked in the Solver
Parameters dialog box.
2. Consider the problem
ELF test
Min 2X2 - 20X + 2XY + Y2 - 14Y +58
s.t. X + 4) = 8
tisord # J# (s.
a. Find the minimum solution to this problem.
b. If the right-hand side of the constraint is increased from 8 to 9, how much do you
expect the objective function to change?
c. Resolve the problem with a new right-hand side of 9. How does the actual change
compare with your estimate?
3. Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demand
for these two cameras are as follows: Ds = demand for the Sky Eagle, Ps is the selling
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6:28 PM
10/2/2019

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