Question 1164173: Assume it costs Microsoft $4,800 to manufacture 8 Xbox 360s and $9,360 to manufacture 16. Obtain the corresponding linear cost function.
C(x) =
What was the cost to manufacture each additional Xbox?
$
Use the cost function to estimate the cost of manufacturing 60 Xboxes.
$
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it cost 4800 to manufacture 8.
it cost 9360 to manufacture 16.
linear equation is y = mx + b.
m is the slope.
b is the y-intercept.
let x = the number manufactured.
let y = the cost.
let(x,y) represent a point on the line.
you have two points.
they are (8,4800) and (16,9360)
m = slope = (y2-y1) / (x2-x1)
let (x1,y1) = (8,4800) and let (x2,y2) = (16,9360)
slope = m = (y2-y1)/(x2-x1) = (9360-4800)/(16-8) = 4560/8 = 570
equation becomes y = 570*x + b
to find b, replace x and y with one of the points.
i chose (8,4800)
equation becomes 4800 = 570 * 8 + b
subtract 570 * 8 from both sides of the equation and simplify to get 4800 - 4560 = b
solve for b to get b = 240
equation becomes y = 570 * x + 240
answers to your questions are:
equation is y = 570 * x + 240
cost to manufacture each additional xbox is 570 (the slope of the equation)
the cost to manufacture 60 xboxes is 570 * 60 + 240 = 34,440.
all this can be seen on the graph which shows the key points of (0,240) which is the y-intercept, (8,4800), (9,9360) and (60,34440).
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