An investment company currently has $$1$ million dollar available for investment in five different stocks. The

company wants to maximize the interest earned over the next year. The five investment possibilities along with

the expected interest earned are shown below. To manage risk, the investment firm wishes to have at least $35\%$ of

the investment in stocks A and B$.$ Furthermore, no more than $15\%$ of the investment may be in stock E$.$

Investment Expected Interest Earned $(\%)$

Stock A $7$

Stock B $9$

Stock C $8$

Stock D $10$

Stock E $11$

Sensitivity Report

Adjustable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$$4$ Stock A $0-0\mathrm{.}020\mathrm{.}070\mathrm{.}021$E$+30$

$C$$4$ Stock B $35000000\mathrm{.}090\mathrm{.}010\mathrm{.}02$

$D$$4$ Stock C $0-0\mathrm{.}020\mathrm{.}080\mathrm{.}021$E$+30$

$E$$4$ Stock D $50000000\mathrm{.}10\mathrm{.}010\mathrm{.}01$

$F$$4$ Stock E $15000000\mathrm{.}111$E$+300\mathrm{.}01$

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$G$$7$ Constraint $110000000\mathrm{.}110000001$E$+30500000$

$G$$8$ Constraint $2350000-0\mathrm{.}01350000500000350000$

$G$$9$ Constraint $31500000\mathrm{.}01150000500000150000$

Use the Sensitivity Report to answer the following questions:

$1.$

a$.$ What is the optimal total expected interest earned for next year?

b$.$ What is the dollar amount that should be invested in each stock?

c$.$ Which constraints are binding? Which constraints are not binding?

d$.$ Is the solution to the problem unique or are there alternate optimal solutions?

e$.$ Does the optimal solution call for investing the entire $$1,000,000\mathrm{.}00?$

$2.$

a$.$ What would be the impact on the optimal allocation if the expected interest earned on stock A decreases to $6\%?$

b$.$ What would be the impact on the optimal allocation if the expected interest earned on stock A increases to

$10\%?$

c$.$ What should the minimal expected interest earned for stock C be before it would be desirable to invest in this

particular stock?

d$.$ What would be the impact on the optimal allocation and the objective function value if the expected interest

earned on stock B decreases by $1\mathrm{.}5\%?$

$3.$

a$.$ Suppose that the amount of money available for investment decreases by $$100,000.$ What impact would this

have on the current optimal objective function value?

b$.$ Suppose that total investment in stocks A and B must be at least $45\%$ of the total amount available for

investment $($i$.$e$.,$ $$450,000).$ What impact would this have on the current optimal objective function value?

c$.$ Suppose that the total investment in stocks A and B must be at least $40\%$ of the total amount available for

investment. What impact would this have on the current optimal objective function value?

d$.$ Assume that no more than $25\%$ of the investment may be in stock E$.$ What impact would this have on the

current optimal objective function value?