SOLUTION: 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 l

Question 100758: 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 oberobic(2302) (Show Source):
You can put this solution on YOUR website!
Imagine that C, the total cost, is plotted on the y-axis; and x, the number of items, is plotted on the x-axis. So the given information defines two points: (100,10000) and (300,22000). Let's divide everything by 100 to get rid of these pesky 00s, but remember the numbers would then be in hundreds of dollars, not dollars. So, we have (1,100) and (3,220).
The slope = (y2-y1)/(x2-x1) = (220-100)/(3-1) = 120/2 = 60. That is a steep line, sloping up to the right.
The general equation of a line is y = mx + b, so in our case it is y = 60x + b.
We know that one point is (1,100), so we substitute: 100 = 60(1) + b, so b = 40.
y = 60x + 40.
To correct for the earlier division by 100, the constant 40 needs be multiplied by 100, so the final equation is:
y = 60x + 4000.
ALWAYS check!
x=100: y = 60*100 + 4000 = 10,000, which is what we were given.
x=300: y = 60*300 + 4000 = 22,000, which is what we were given.
Check.