A DVD producer has fixed costs (factory, machinery, and money paid to the recording artist) of $406,000. Additionally, for every DVD produced, the company spends $5 for materials and labor. The DVDs can be sold for $12 each.

Question

A DVD producer has fixed costs (factory, machinery, and money paid to the recording artist) of $406,000.  Additionally, for every DVD produced, the company spends $5 for materials and labor.  The DVDs can be sold for $12 each.
a) Define a function, which gives the producer’s total cost in terms of the number of DVDs produced.

b) Define another function, which gives the total revenue in terms of the number of DVDs sold.

(c) Graph both the functions on the same set of axes.
  
(d) Locate the point of intersection.

(e) How many DVDs must they produce so that cost equals revenue (they breakeven)?

Steve · Answer

c = 406000 + 5n r = 12n at breakeven, c=r 406000+5n=12n 406000=7n n = 58000