Question

A furniture manufacturer can sell dining-room tables for $70 apiece. The manufacture‘s total cost consists of a fixed overhead of $8,000 plus production costs of $30 per table.

a. How many tables must be the manufacturer sell to break even?

b. How many tables must the manufacturer sell to make a profit of $6,000?

c. What will the manufacturer’s profit or loss if 150 tables are sold?

Answer 1

Solution

Price$=70$

Let $T$ represent the total number of tables sold.

Total revenue

$TR=70T$

Total cost $TC=Fixed~cost +Variable ~cost$

$TC=8,000+30T$

(a) To break even total revenue must equal total cost

$TR=TC$

$70T=8,000+30T$

solving for $T$

$T= 40$ tables

(b) To make a profit of $6,000$

$TR=TC+6,000$

$70T=(8,000+30T)+6,000$

Solving for $T$

$T =350$ tables

(c) Net gain from 150 tables

$TR=70T=70\times 150=10,500$

$TC=8,000+30\times150=12,500$

Net gain $=TR-TC$

$=10,500-12,500$

$=-2,500$

The manufacturer will have a loss of $2,500$ if only 150 tables are sold.