Assume it costs Microsoft $4,300 to manufacture 7 Xbox 360s and $8,290 to manufacture 14. Obtain the corresponding linear cost function.
C(x)= (what formula do I use to get the cost function, because I can't get it)
What was the cost to manufacture each additional Xbox? (Do I need the cost function to solve this?)
Use the cost function to estimate the cost of manufacturing 60 Xboxes.(Do I just plug it in the cost function?)
Thank you.
To obtain the corresponding linear cost function, we can use the formula for a straight line, which is given by:
y = mx + b
where y is the dependent variable (cost in this case), x is the independent variable (the number of Xboxes), m is the slope of the line, and b is the y-intercept.
To find the slope (m) of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the two points given:
(x1, y1) = (7, 4300)
(x2, y2) = (14, 8290)
Plugging in the values:
m = (8290 - 4300) / (14 - 7)
m = 3990 / 7
m = 570
Now that we have the slope, we can find the y-intercept (b) by substituting one of the given points and the slope into the original equation:
4300 = 570 * 7 + b
Solving for b:
b = 4300 - 3990
b = 310
Therefore, the linear cost function can be expressed as:
C(x) = 570x + 310
Now we can answer the remaining questions:
1. What was the cost to manufacture each additional Xbox?
To find the cost to manufacture each additional Xbox, we can calculate the difference in cost between two adjacent values of x. In this case, we can use the formula C'(x) = C(x + 1) - C(x). Let's plug in the values:
C'(x) = (570(x + 1) + 310) - (570x + 310)
C'(x) = 570x + 570 + 310 - 570x - 310
C'(x) = 570
Therefore, the cost to manufacture each additional Xbox is $570.
2. Use the cost function to estimate the cost of manufacturing 60 Xboxes.
To estimate the cost of manufacturing 60 Xboxes, we can plug in x = 60 into the cost function:
C(60) = 570(60) + 310
C(60) = 34200 + 310
C(60) = 34510
Therefore, the estimated cost of manufacturing 60 Xboxes is $34,510.