Assume that the number of units sold of a product is given by 100-0.5p+26√A , where P is the price (in dollars) charged for the product and A is the amount spent on advertising (in thousands of dollars). Each unit of the product costs $5 to produce. Use a 2-way data table to find the combination of price and advertising that maximizes profit. You must pick out the ranges for the data table, and use trial and error to zoom in on the correct ranges that include the optimal price/advertising combination. (To validate your model, if the price is $10, and the advertising dollars are $10,000, then the profit should be about -$9 thousand [so you’d lose money]) .
Hint: Recall the units of A in the formula. It’s in thousands. So that if you spend 5000 in advertising, then your formula would be 100-0.5p+26√5 . However, you still incur the full 5000 as part of your costs.
Turn in your spreadsheet and answer the following.
1) What is the optimal price/advertising combination?
2) Describe in words why the above equation ( 100-0.5p+26√A) makes sense in a way a non-supply chain person would understand. Plot the relationship of demand vs. price and demand vs. advertising dollars in a rough handsketch as part of this. What might be the reason behind these relationships? Describe.