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 Lady$-$Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. 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 Lady$-$Sport engine requires $3$ hours of manufacturing time.

The Des Moines plant has $2,100$ 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 Lady$-$Sport frame is more complex and the supplier can only provide up to $240$ Lady$-$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 Lady$-$Sport model. A maximum of $850$ hours of assembly and testing time are available for the next

production period. The company's accounting department projects a profit contribution of $$2,400$ for each EZ$-$Rider produced and $$1,800$ for each Lady$-$Sport produced.

$($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. $($Let $E$ represent the EZ$-$Rider model and let $L$ represent the Lady$-$Sport model.$)$

Engine manufacturing time

Assembly and testing time

$($b$)$ Solve the problem graphically. What is the optimal solution?

$(E,L)=(,)$

$($c$)$ Which constraints are binding? $($Select all that apply.$)$

Engine manufacturing time

Lady$-$Sport maximum

Assembly and testing time