Question

A manufacturer has a monthly fixed cost of $50,000 and a cost of $30 for each unit produced. Each unit is sold for $70.
Write the cost function for this manufacturer.

Write the revenue functionfor this manufacturer.

Determine the number of units that need to be produced and sold for this manufacturer to break even.

Answer 1

Let x=number of units produced
Let C=Cost
Let R=Revenue

C=30x+50,000 This is the Cost Function

R=70x This is the Revenue Function

R=C This will give you the breakeven

70x=30x+50,000
40x=50,000
x=1250 These are the number of units produced and sold to breakeven

R-C=0 which is the breakeven

This can be checked out by the following:

R=(1250)(70)=$87,500

C=(1250)(30)+50,000=37,500+50,000=$87,500

R-C=$87,500-$87,500=0