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Question

A company manufactures tables. They spend $12,000 on machinery. For each table made, they use $74 of raw materials and $105 for finishing costs. Tables are sold for $299 each. Find the linear equation for the profit. Also find the number of tables the company needs to make to break ever.

Answer 1

Profit is found by subtracting costs from revenue. The cost per table is 74+105=179. The total costs are 12000+179*x, where x is the number of tables. The revenue is 299*x. Then the profit P is:

  P=299x - (12000+179x)   (Profit)

  P=299x - 12000 - 179x.    (subtract both terms in parentheses)

  P=120x - 12000               (subtract like terms)

This is the simplified profit equation.

 

The company breaks even when the profit reaches 0,

120x -12000 = 0

120x = 12000      (add 12000 to both sides)

x = 100               (divide both sides by 120)

So, the company breaks even at 100 tables, after which profit is positive.