OECS Motorcycles $($OM$)$ manufacturers 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. OECS produces the engines for both models at its St Vincent, plant. Each EZ$-$Rider engine

requires $6$ hours of manufacturing time and each Lady$-$Sport engine requires $3$ hours of manufacturing

time. The St Vincent plant has $2100$ hours of engine manufacturing time available for the next

production period. OECS'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 $280$ 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 $1$ 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 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 to

maximize total profit contribution

B$)$ Graph the feasible region $($PLEASE SHOW GRAPH $)$

C$)$ Determine the coordinates of each extreme point

D$)$ What is the optimal solution