Question: We are determining whether to invest in a t-shirt printing machine. The cost function per t-shirt is identified to be the following: y=ln(X+1). Fixed costs associated are a step function based on area needed. For each 1000 shirts, the cost associated with storage space is $1000 (z=1000X). Note:

The step function is as follows:

z(x) = 1000 for x from 1 to 1000

=2000 for x from 1001 to 2000

=3000 for x from 2001 to 3000

a. What is the total cost function?

b. Find the optimal number of shirts produced to minimize the cost function.