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.
:
Find the cost to make each individual item
{{{42/32}}} = $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( 300, 200, -20, 100, -20, 200, 1.3125x+45, 2x, 132) }}}
:
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