Look at the posted picture. Follow these directions (only).
Determine the objective function and constraints using the variables ...
Let E = number of units of the EZ-Rider produced
L = number of units of the Lady-Sport produced
Now, showing work manually for every step, complete the following:
Graph each constraint
Identify the Feasible Region
Find the optimal point on the graph by graphing the Objective Function
Identify the binding constraints
Use either the addition, subtraction, or substitution method to find that exact point (Dec. Var. Values)
Use the decision variable values to calculate the Objective Function Value
Calculate the Slack or Surplus for each constraint (Make sure and indicate if the calculated amount is Slack or Surplus)
Embassy Motorcycles (EM) 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 ady-Sport model is slightly larger, uses a more traditional engine, easy to balance.
The L is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each ider engine requires 6 hours of manufac- turing 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 produc- tion 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 re- quires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maxi mum 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 contribu- tion to profit.
b. Solve the problem graphically. What is the optimal solution?
c. Which constraints are binding?