SOLUTION: A manufacturer produces items and sells them for $2 per item. It costs $42 to make 32 items and the daily operational overhead is $45.00. a) Graph the cost and revenue functions

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A manufacturer produces items and sells them for $2 per item. It costs $42 to make 32 items and the daily operational overhead is $45.00. a) Graph the cost and revenue functions      Log On


   

Question 1037818: A manufacturer produces items and sells them for $2 per item. It costs $42 to make 32 items and the daily operational overhead is $45.00.
a) Graph the cost and revenue functions on the same set of axes.
b) Find the break-even point using algebra not the graph.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A manufacturer produces items and sells them for $2 per item.
It costs $42 to make 32 items and the daily operational overhead is $45.00.
:
Find the cost to make each individual item
42%2F32 = $1.3125
x = no. of items made
Cost
C(x) = 1.3125x + 45 (Red)
Revenue
R(x) = 2x (green)
:
(a) Graph the cost and revenue functions on the same set of axes.
+graph%28+300%2C+200%2C+-20%2C+100%2C+-20%2C+200%2C+1.3125x%2B45%2C+2x%2C+132%29+
:
b) Find the break-even point using algebra not the graph.
Rev = Cost
2x = 1.3125x + 45
2x - 1.3125x = 45
.6875x = 45
x = 45/.6875
x = 65.46 ~ 66 items to at least break even
:
Confirm
2(66) = $132 (Blue line)
1.3125(66) + 45 = $131.63