Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a numberof clients. A particular portfolio consists of U shares of U$.$S$.$ Oil and H shares ofHuber Steel. The annual return for U$.$S$.$ Oil is $$3$ per share and the annual return forHuber Steel is $$5$ per share. U$.$S$.$ Oil sells for $$25$ per share and Huber Steel sells for$$50$ per share. The portfolio has $$80,000$ to be invested. The portfolio risk index$(0\mathrm{.}50$ per share of U$.$S$.$ Oil and $0\mathrm{.}25$ per share for Huber Steel$)$ has a maximum of $700.$In addition, the portfolio is limited to a maximum of $1000$ shares of U$.$S$.$ Oil. The linearOptimal Objective Value $=8400\mathrm{.}00000$Variable Value Reduced Cost$----------------------------------------------$U $800\mathrm{.}000000\mathrm{.}00000$H $1200\mathrm{.}000000\mathrm{.}00000$Constraint Slack$/$Surplus Dual Value$----------------------------------------------10\mathrm{.}000000\mathrm{.}0933320\mathrm{.}000001\mathrm{.}333333200\mathrm{.}000000\mathrm{.}00000$Objective Allowable AllowableVariable Coefficient Increase Decrease$------------------------------------------$U $3\mathrm{.}000007\mathrm{.}000000\mathrm{.}50000$H $5\mathrm{.}000001\mathrm{.}000003\mathrm{.}50000$RHS Allowable AllowableConstraint Value Increase Decrease$------------------------------------------180000\mathrm{.}0000060000\mathrm{.}0000015000\mathrm{.}000002700\mathrm{.}0000075\mathrm{.}00000300\mathrm{.}0000031000\mathrm{.}00000$ Infinite $200\mathrm{.}00000$programming formulation that will maximize the total annual return of the portfolio isas follows:Max $3$U $+5$H Maximize total annual returns.t$\mathrm{.}25$U $+50$H $<=80000$ Funds available$0\mathrm{.}50$U $+0\mathrm{.}25$D$<=700$ Risk maximum$1$U $<=1000$ U$.$S$.$ Oil maximumThe computer solution of this problem is shown in Figure $3\mathrm{.}14.$a$.$ What is the optimal solution, and what is the value of the total annual return?b$.$ Which constraints are binding? What is your interpretation of these constraints interms of the problem?c$.$ What are the dual values for the constraints? Interpret each.d$.$ Would it be beneficial to increase the maximum amount invested in U$.$S$.$ Oil? Why orwhy not?