The linear programming formulation that will maximize the total annual return of the portfolio is as follows.

Max $3U+5H$ Maximize total annual return

$s.t.$

$25U+50H80,000$ Funds available

$0\mathrm{.}50U+0\mathrm{.}25H700$ Risk maximum

$1U1,000U.S.$ Oil maximum

$U,H0$

The computer output is shown in picture.

$($a$)$ What is the optimal solution, and what is the value of the total annual return $($in $$)?$

U $-?$

H $-?$

estimated annual return$-?$ $

$($b$)$ Which constraints are binding? What is your interpretation of these constraints in terms of the problem? $($Select all that apply.$)$

a$)$ Constraint $1.$ All funds available are being utilized.

b$)$ Constraint $2.$ The maximum permissible risk is being incurred.

c$)$ Constraint $3.$ All available shares of U$.$S$.$ Oil are being purchased.

d$)$ None of the constraints are binding.

$($c$)$What are the dual values for the constraints? Interpret each. $($Round your answers to two decimal places.$)$

constraint $1$

a$)$ Constraint $1$ has a dual value of $5.$ If an additional dollar is added to the available funds, the total annual return is predicted to increase by $$5.$

b$)$ Constraint $1$ has a dual value of $3.$ If an additional dollar is added to the available funds, the total annual return is predicted to increase by $$3.$

c$)$ Constraint $1$ has a slack of $$200.$ Additional dollars added to the available funds will not improve the total annual return.

d$)$ Constraint $1$ has a dual value of $0\mathrm{.}09.$ If an additional dollar is added to the available funds, the total annual return is predicted to increase by $$0\mathrm{.}09.$

e$)$Constraint $1$ has a dual value of $1\mathrm{.}33.$ If an additional dollar is added to the available funds, the total annual return is predicted to increase by $$1\mathrm{.}33.$

constraint $2$

a$)$ Constraint $2$ has a dual value of $5.$ If the risk index is increased by $1,$ the total annual return is predicted to increase by $$5.$

b$)$ Constraint $2$ has a dual value of $3.$ If the risk index is increased by $1,$ the total annual return is predicted to increase by $$3.$

c$)$ Constraint $2$ has a slack of $200.$ Allowing additional risk will not improve the total annual return.

d$)$ Constraint $2$ has a dual value of $0\mathrm{.}09.$ If the risk index is increased by $1,$ the total annual return is predicted to increase by $$0\mathrm{.}09.$

e$)$ Constraint $2$ has a dual value of $1\mathrm{.}33.$ If the risk index is increased by $1,$ the total annual return is predicted to increase by $$1\mathrm{.}33.$

constraint $3$

a$)$ Constraint $3$ has a dual value of $5.$ If the maximum number of shares of U$.$S$.$ Oil is increased by $1,$ the total annual return is predicted to increase by $$5.$

b$)$ Constraint $3$ has a dual value of $3.$ If the maximum number of shares of U$.$S$.$ Oil is increased by $1,$ the total annual return is predicted to increase by $$3.$

c$)$ Constraint $3$ has a slack of $200$ shares. Raising the maximum number of shares of U$.$S$.$ Oil will not improve the total annual return.

d$)$ Constraint $3$ has a dual value of $0\mathrm{.}09.$ If the maximum number of shares of U$.$S$.$ Oil is increased by $1,$ the total annual return is predicted to increase by $$0\mathrm{.}09.$

e$)$ Constraint $3$ has a dual value of $1\mathrm{.}33.$ If the maximum number of shares of U$.$S$.$ Oil is increased by $1,$ the total annual return is predicted to increase by $$1\mathrm{.}33.$

$($d$)$Would it be beneficial to increase the maximum amount invested in U$.$S$.$ Oil? Why or why not?

a$)$ Yes, each additional share increases the profit by $$1\mathrm{.}33.$

b$)$ Yes, each additional share increases the profit by $$200\mathrm{.}00.$

c$)$ Yes, each additional share increases the profit by $$0\mathrm{.}09.$

d$)$ No$,$ increasing the maximum shares does not affect the optimal value.