Sales growth: In this exercise we develop a model for the growth rate G, in thousands of dollars per year, in sales of a product as a function of the sales level s, in thousands of dollars.30 The...

Sales growth: In this exercise we develop a model for the growth rate G, in thousands of dollars per year, in sales of a product as a function of the sales level s, in thousands of dollars.30 The model assumes that there is a limit to the total amount of sales that can be attained. In this situation we use the termunattained salesfor the difference between this limit and the current sales level. For example, if we expect sales to grow to 3 thousand dollars in the long run, then 3 − s gives the unattained sales. The model states that the growth rate G is proportional to the product of the sales levels and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run.

a. Find a formula for unattained sales.

b. Write an equation that shows the proportionality relation for G.

c. On the basis of the equation from part b, make a graph of G as a function of s.

d. At what sales level is the growth rate as large as possible? e. What is the largest possible growth rate?