Determine the equations for each of the three constraints that are plotted on the attached “Graph 1,” showing all work necessary to arrive at the equations.

Graphical models enable a manager to visualize the objective function (profit line), constraints, and possible solutions to a given problem, and to make more informed decisions based on that information. 

Task: 

A. Determine the equations for each of the three constraints that are plotted on the attached “Graph 1,” showing all work necessary to arrive at the equations.

1. Identify each constraint as a minimum or a maximum constraint.

B. Determine the total contribution to profit if the company produces a combination of cases of Brand X and Brand Y that lies on the purple objective function (profit line) as it is plotted on the attached “Graph 1.” 

C. Determine how many cases each of Brand X and of Brand Y you recommend should be produced during each production period for optimum production if Company A wants to generate the greatest amount of profit, showing all of your work.

D. Determine the total contribution to profit that would be generated by the production level you recommend in part C, showing all of your work.

See the attached case study:

Solution

A. The three constraints in Graph 1 are as follows:

1. Minimum constraint for Brand X: This constraint is represented by the line that runs parallel to the y-axis and is labeled as Xmin. The equation for this constraint is: X >= Xmin (X represents the number of cases of Brand X produced)
2. Maximum constraint for Brand Y: This constraint is represented by the line that runs parallel to the x-axis and is labeled as Ymax. The equation for this constraint is: Y <= Ymax (Y represents the number of cases of Brand Y produced)
3. Maximum constraint for the total production: This constraint is represented by the line that is sloping downward and is labeled as Zmax. The equation for this constraint is: X + Y <= Zmax (Zmax represents the maximum total production)

B. The purple objective function (profit line) represents the total contribution to profit for the company. In order to determine the total contribution to profit for a given combination of Brand X and Brand Y, we would need to know the specific profit values for each product. Without this information, it is not possible to determine the total contribution to profit for a given combination of Brand X and Brand Y that lies on the purple objective…Order a customized and more comprehensive answer here