SOLUTION: Hello, I need help with this question, please! When a manufacturer makes 700 units it costs $2,500. When they make 1200 units, it costs $4,000. Assuming the cost is linear, and

Algebra ->  Finance -> SOLUTION: Hello, I need help with this question, please! When a manufacturer makes 700 units it costs $2,500. When they make 1200 units, it costs $4,000. Assuming the cost is linear, and       Log On


   



Question 1109230: Hello, I need help with this question, please!
When a manufacturer makes 700 units it costs $2,500. When they make 1200 units, it costs $4,000. Assuming the cost is linear, and they sell the product for $50 per unit.
Find the profit function and use it to find the break-even point.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the Cost, C, on the vertical axis
Plot number of units, n, on the horizontal axis
--------------
You are given 2 points on a straight line
( 700, 2500 )
( 1200, 4000 )
Use the general point-slope formula to
find the equation:
+%28+C+-+2500+%29+%2F+%28+n+-+700+%29+=+%28+4000+-+2500+%29+%2F+%28+1200+-+700+%29+
+%28+C+-+2500+%29+%2F+%28+n+-+700+%29+=+1500+%2F+500+
+%28+C+-+2500+%29+%2F+%28+n+-+700+%29+=+3+
+C+-+2500+=+3%2A%28+n+-+700+%29+
+C+=+3n+-+2100+%2B+2500+
+C+=+3n+%2B+400+
-------------------------------
Let Profit = +P+
+P+=+50n+-+C+
+P+=+50n+-+3n+-+400+
+P+=+47n+-+400+
The break even point is where +P+=+0+
+47n+=+400+
+n+=+8.51+
The break even point would be 9 units
( can't have part of a unit )
-----------------------------------
check:
+C+=+3%2A8.51+%2B+400+
+C+=+25.53+%2B+400+
+C+=+425.53+
+P+=+50n+-+800+
+P+=+50%2A8.51+-+425.53+
+P+=+425%2C5+-+425.53+
close enough