Business Calculus

 
{After you have completed Modules 1 through 3B, provide brief responses to parts “a” and “b” of the items that follow.  The actual data on which the total Cost, Revenue and Profit equations are based are provided, for your information, on the attached spread sheet AQ1(X410)Data(2017).xlsx.  While you may find developing a system graph for the data to be helpful, this is left up to your discretion, and the graph itself will not be graded and need not be provided as part of your solutions.}
After earning your MBA degree, you join a new firm and are assigned to work directly for the Division Director, Consumer Products Division.  During an initial period, you are attached for short periods of time to work with the Line Manager of each of the Division’s three products “#”, “##” and “###”.
One day, the Division Director asks you to informally review the current total Cost “C”, Revenue “R” and Profit “P” models associated with associated with Product line “###”, the Division’s newest, but possibly underperforming, product line.  Among other important questions, the Director would like answers to ones provided below.  [The dependent variables are “C”, “R” or “P”; the independent variable is “x”, the number of units (produced and) sold].  Quadratic “C”, “R” or “P” models provide the “best fit” to the data on which the these models (referenced above), are based.  These models follow:
C = –0.125(x)2 + 300(x)1 + 190,000 with [(R^2)] = 1.0.
R = –0.25(x)2 + 450(x)1 with [(R^2)] = 1.0.
 P = –0.125(x)2 + 150(x)1 – 190,000 with [(R^2)] = 1.0.
a.  [2 pts.] Calculate how many product units “x” should be sold per sales period to maximize this product’s total Profit “P”…then…calculate “Pmax” at this “x” value.  Assume market constraints suggest that 1,400 is the maximum number of product units that actually can be sold per sales period per sales period.
b.  [2 pts.] If internal production or external market constraints were not an issue, determine, if possible, the minimum number of product units “x” that must be produced and sold in order to “break even” (i.e. generate a Profit of $0.00). 
                                                                                                                                                                                                    [AQ1(x410)2017]