Chapter 12.4, Problem 41E

Franchising Marketing researchers have studied the advertising fees that a franchisee (such as the owner of a fast food outlet) pays to the franchisor (the national fast food corporation).

Source: Journal of the Operational Research Society.

1. (a) The researchers postulate that the anticipated sales would be a function of the level of local advertising A chosen by the franchisee of the form

   $S\left(A\right)=c-d{e}^{-\theta A}$

   where c, d and θ are constants such that c > d > 0 and θ > 0. Sketch the graph of this function, and discuss why such a shape seems plausible.

2. (b) The researchers propose hypothetical values c = 60,000 units, d = 50,000 units, and θ = 0.0006. Find the values of S(A) and S' (A) when the level of local advertising is set at $2500.
3. (c) Repeat part (b) using $4000.
4. (d) If you were the franchisee, what decisions might you make on advertising based on the results of parts (b) and (c)?