Question 73425: I am having problems with this one.This is what I have so far.
x=number of items produced
C=cost in dollars
100items=$10,000
300items=$22,000
Business and finance. In planning for a new item, a manufacturer assumes that
the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Since this is a linear equation by assumption, the slope-intercept form can be used. This
equation will be in the form y = mx + b. But we will redefine the variables. Replace
y with C the cost. x will still be used to represent the number of items produced. x will be on
the x-axis and C will be on the y-axis.
.
As the number of items manufactured increases from 100 to 300 units (an increase of 200 items)
the cost goes from $10,000 to $22,000 (an increase of $12,000). The slope of this graph is,
therefore:
.
.
and the 60 represents the dollars that it costs to produce a unit.
.
So far our equation is:
.
.
The question now is how do we calculate b? We can use the fact that when x = 100, then
C = $10,000. Plug these values into the equation and you find:
.
.
This simplifies to:
.
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Subtract 6000 from both sides and you find that
.
.
Plug that value into the equation and you get:
.
.
This is the equation that relates C and x (thenCost and number of items produced).
Notice something interesting. If you produced no items (x = 0) the cost is still $4000.
This probably involves the cost of labor to maintain the assembly line, store the materials,
keep the lights and heat on, and so forth.
.
Hope this helps you to understand the graphing process. You can check the equation out
by letting x = 300 items and see if the cost computes to $22,000 as specified in the problem.
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