Question: Consider the following break-even problem: the cost of producing Q units, c(Q), is described by the curve
c(Q) = 48Q[1 - exp(-.08Q)],
where Q is in hundreds of units of items produced and c(Q) is in thousands of dollars.
a. Graph the function c(Q). What is its shape? What economic phenomenon gives rise to a cumulative cost curve of this shape?
b. At what production level does the cumulative production cost equal $1,000,000?
c. Suppose that these units can be purchased from an outside supplier at a cost of $800 each, but the firm must invest $850,000 to build a facility that would be able to produce these units at a cost c(Q). At what cumulative volume of production does it make sense to invest in the facility?