Q$1.$

$11.$ Solving Linear Program with Graphical Solution Method. Solve the following linear program using the graphical solution procedure. LO $2,4$

Max $5A+5B$

$s.t.$

$1A100$

$1B80$

$2A+4B400$

$A,B0$

Q$2.$

$23.$ 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 make 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, lowa, 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. Embassy's 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 requires $2$ 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 company's accounting department projects a profit contribution of $$2400$ for each EZ$-$Rider produced and $$1800$ for each Sport produced. LO $2,4,5,6$

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?