Reference no: EM132460831

In addition to selling price, product sales can be affected by a number of other factors such as marketing expenses, product features, actions of competitors, etc. Sometimes, mathematical models can help in determining the effect of these factors on company sales and profits, and therefore in developing the best business decisions (pricing, expenditures, production volumes, etc.).

Suppose that the demand (sales) for a product depends upon its price and the marketing expenditure, and can be represented as follows:

Sales = (Base Sales)(Price)-e(Marketing Expenditure)a = B P-e Ma

where B = base sales P = selling price

e = price elasticity

M = marketing expenditure

a = marketing expenditure elasticity

Preliminary statistical analysis of data suggests that B = 200,000, e = 2.5, and a = 0.2. Suppose also that the cost of producing the parts is constant, and denoted by C. With the current production technology, C is equal to $30.00/unit.

As product manager, you must determine the optimal strategy for your company's pricing, marketing, and production functions by maximizing the profit.

Questions:

1A. Use the Data Table Approach to estimate the optimal selling price, marketing expense, and profit for your firm.

1B. Draw a three-dimension (two decision variables) graph to approximate optimal selling price, marketing expense, and profit for your firm. (Hint: You may use the result of the above Data Table to draw this graph if preferred, although not required.)