Problems:#$1.$ Solving Linear Program with Solver Method. Solve the following linear program using Sover in Excel solution procedure. $($MLO $2\mathrm{.}2)$Max$5$A $+5$Bs$.$t$\mathrm{.}1$A $1001$B $802$A $+4$B $400$A$,$ B $0$a$.$ What is the value of variables A and B$?$b$.$ What is the value of the objective function? #$2.$ The Par, Inc., Problem $($revisited$).$ Refer to the Par, Inc., problem described in Section $2\mathrm{.}1.$ Suppose that Par, Inc.s management encounters the situations described below. If Par, Inc., encounters each of these situations separately, what is the optimal solution and the total profit contribution for each situation described? $($MLO $2\mathrm{.}12\mathrm{.}3)$a$.$ The accounting department revised its estimate of the profit contribution for the deluxe bag to $$18$ per bag.b$.$ A new low$-$cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $$20$ per bag. $($Assume that the profit contribution of the deluxe bag is the original $$9$ value.$)$c$.$ New sewing equipment is available that would increase the sewing operation capacity to $750$ hours. $($Assume that $10$A $+9$B is the appropriate objective function.$)$#$3.$ Number of Motorcycles to Produce. Embassy Motorcycles $($EM$)$ manufactures two lightweight motorcycles designed for easy handling and safety. The EZ$-$Rider model has a new engine and a low profile that makes it easy to balance. The Sport model is slightly larger and uses a more traditional engine. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ$-$Rider engine requires $6$ hours of manufacturing time, and each Sport engine requires $3$ hours of manufacturing time. The Des Moines plant has $2100$ hours of engine manufacturing time available for the next production period. Embassys motorcycle frame supplier can supply as many EZ$-$Rider frames as needed. However, the Sport frame is more complex, and the supplier can only provide up to $280$ Sport frames for the next production period. Final assembly and testing require $2$ hours for each EZ$-$Rider model and $2\mathrm{.}5$ hours for each Sport model. A maximum of $1000$ hours of assembly and testing time are available for the next production period. The companys accounting department projects a profit contribution of $$2400$ for each EZ$-$Rider produced and $$1800$ for each Sport produced. $($MLOs $2\mathrm{.}12\mathrm{.}3)$a$.$ Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit.b$.$ Solve the problem graphically. What is the optimal solution?c$.$ Which constraints are binding? #$4.$ Investments for a College Savings Fund. Julia Johnson has been accumulating savings for years to put toward her children's future college educations. She would now like to set up a college$-$savings fund for her two children. The college$-$savings fund has two investment options: $(1)$ a bond fund and $(2)$ a stock fund. The projected returns over the life of the investments are $6\%$ for the bond fund and $10\%$ for the stock fund. Whatever portion of her accumulated savings that she finally decides to commit to the college$-$savings fund, she wants to invest at least $30\%$ of that amount in the bond fund. In addition, she wants to select a mix that will enable her to obtain a total return of at least $7\mathrm{.}5\%.($MLOs $2\mathrm{.}22\mathrm{.}3).$Reminder that you need to include a constraint where the percentages add up to $1.$a$.$Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives.b$.$Solve the problem using the graphical solution procedure.