In 2011, the Cornucopia Products Company (CPC) realized $100,000 in profits. Their 2011 customer base of 20,000 is relatively stable. Based on past trends, they can expect to retain that customer base in 2012. If they make no additional changes in marketing or R & D, then it is reasonable to expect their customer base in 2012 will be remain the same. Increasing their profits will depend on generating new customers either through successful advertising campaigns and or attractive fruits of research & development. The total customer base C in 2012 will be the retained customers plus any new customers. If C is their 2012 customer base in thousands, then their profit P (in thousands of dollars) is given by
P = 0.01C^2 + 7C – 44
In 2012, CPC can choose to invest some part of its 2011 profits in one or more forms of advertising. In everything on this card, X = money (in thousands of dollars) invested in that form of advertising, and N is the number of new customers (in thousands), on average, that form of advertising is likely to generate in 2012.
1) Print Media
Investment: no more than $10,000, due to sharply diminishing returns above that threshold.
If X < 10, N = X/2
2) TV & Movie advertising
Investment: minimum of $15,000
If X > 15, N = 2X/3 – 10
3) Web-based advertising
Investment: no lower or upper limit
N = X/4
In CPC's Research and Development (R & D), many new products have been developed in the past, contributing to its financial success. In 2012, CPC has already allocated a small baseline budget to ongoing R & D, without any expectation that those results will bear fruit in this calendar year. Beyond that, CPC has to decide about whether to put more money from its 2011 profits into two ongoing projects.
Project A has been in development for a little over a year. It is close to completion. The most reliable data about Project A suggest if CPC makes a $10000 investment in 2011, there's an 80% chance of producing a new product that would add 5,000 new customers in 2012; if CPC makes a $30,000 investment, there's a 20% chance of producing a suite of new products that would add 30,000 new customers.
Project B is a relatively new product, involving some cutting edge technology. It's very expensive, and the results are uncertain. The most reliable data about Project B suggest if CPC makes a $40000 investment in 2011, there's a 40% chance that the new products would add 50,000 new customers in 2012.