Problem #$1($problem #$23$ in chapter $2)$

Embassy Motorcycle $($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 mode is slightly larger, uses more traditional engine, and is specifically designed to appeal

to women riders. 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 Lady$-$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 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$-$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 $($LP$)$ 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 $($clearly show the feasible region and the profit line$).$

i$.$ What is the optimal solution $($i$.$e$.$ how many units should EM produced from each model and what is

the resulting contribution to profit?$)$

ii$.$ Briefly explain how you determined the optimal solution.

iii. Which constraints are binding and which are non$-$binding? Explain why and what it means in terms

of use of resources.

$($c$)$ Solve the LP with the Excel Solver and verify your answers to questions in part $($b$)$