Question

A company sells desks for $155 each. To produce a batch of x desks, there is a cost of $83 per desk and a fixed or setup cost of $9,300 for the entire batch. Determine a function that gives the profit in terms of the number of desks produced. What is the least number of desks the company can sell in order to have a profit of $11,000?

Answer 1

If the number of desks sold is represented by "d", then the revenue (R) is
R = 155d
and the costs (C) is
C = 9300 +83d

The profit (P) is the difference between revenue and cost.
P = R - C
P = 155d -(9300 +83d)
P = 72d -9300
We want the profit to be a minimum of 11,000, so we have
11000 ≤ 72d - 9300
20300 ≤ 72d
281 17/18 ≤ d

The company must sell at least 282 desks to have a profit of $11,000.