Problem 1

Zippy motorcycle manufacturing produces two popular pocket bikes (miniature motorcycles with 49cc engines): the Razor and the Zoomer. In the coming week, the manufacturer wants to produce up to 700 bikes and wants to ensure the number of Razors produced does not exceed the number of Zoomers by more than 300. Each Razor produced and sold results in a profit of $70 while each Zoomer results in a profit of $40. The bikes are identical mechanically and only differ in the appearance of the polymer based trim around the fuel tank and seat. Each Razor's trim requires 2 pounds of polymer and 3 hours of production time while each Zoomer requires 1 pound of polymer and 4 hours of production time. Assume that 9,700 pounds of polymer and 2,400 labor hours are available for production of these items in the coming week. Formulate an LP model for this problem: clear define the decision variables, construct the objective function, formulate the constraints

Step 1: Clearly define the decision variables-1 point

Step 2: Construct the objective function-1 point

Step 3: Formulate the constraints-4 points

Problem 2

Consider the following linear programming problem:

Maximize 6x+5y (OBJ)

Subject to x+y6 (1)

2x+y8 (2)

y5 (3)

x,y0

What is the optimal solution to this problem? What is the optimal value of the objective function? Solve this model by using graphical analysis based on the Corner Point Solution Method.

Answer questions below.

2.1. Clearly plot and label the constraints. Show your calculations for drawing constrain line. The solution without calculation will not be accepted. (3 points)

2.2. Develop and shade the feasible region. Use graph paper. (2 points)

2.3. Compute all the corner points or extreme points and their coordinates (i.e. the values of x and y). The solution without calculation will not be accepted. (2 points)

2.4. Determine the optimal solution (i.e. the values of x and y) using corner points method. Why your solution is optimal? (2 points)

2.5 Compute the value of the objective function at the optimal solution. (2 points)

2.6. Identify the binding and non-binding constraint(s). Explain why? (2 points)

2.7 Is coordinate (4, 2) feasible solution? Explain Why? The solution without any explanation will not be accepted (1 point)

Show the graph with the optimal point.