year evenly distributed across the year. Each widget cost $b dollars in material and
manufacturing costs to make. Every time you do a production run to make some widgets, you
incur a set-up cost of P dollars. Any widgets awaiting sale must be stored and thus incur an
average storage fee of c dollars per widget per year. Let x be the size of each production run
(i.e. x is the number of widgets per production run).
a) Write a cost function C(x) and explain each term in the equation and how it was determined.
b) Write down any constraints on the allowable values of x.
c) Determine a formula for the value of x that minimizes total annual cost. Show all of your
work.
d) Prove that your formula actually corresponds to the global minimum cost.
e) Write down a formula for the number of production runs per year as a function of x.