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?

Question

Mathematics

Sherlock

13 November, 15:31

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?

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Londyn Williamson · 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.