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.

if m = cost/unit and b = fixed cost,

c = mx+b

8290 = 14m + b
4300 = 7m + b
so,

3990 = 7m
m = 570
b = 310

cost c = 570x + 310

To obtain the corresponding linear cost function, we need to find the relationship between the number of Xbox 360s manufactured and the cost associated with manufacturing them.

Given the information provided, we can observe that when Microsoft manufactures 7 Xbox 360s, the cost is $4,300, and when they manufacture 14 Xbox 360s, the cost is $8,290.

To find the slope of the linear cost function, we can use the formula:

Slope = (Change in cost) / (Change in quantity)

Let's calculate the slope using the two data points:

Slope = (8290 - 4300) / (14 - 7) = 3990 / 7 = 570

Therefore, the slope of the linear cost function is 570.

Now, we need to find the y-intercept of the cost function. We can choose any data point and use the formula:

y = mx + b

Using the point (7, 4300):

4300 = 570 * 7 + b
4300 = 3990 + b
b = 310

Therefore, the y-intercept of the linear cost function (b) is 310.

Putting it all together, the linear cost function is:

C(x) = 570x + 310

Now, let's move on to the other questions:

1. What was the cost to manufacture each additional Xbox?

To find the cost to manufacture each additional Xbox, we need to find the slope of the linear cost function. From the calculation above, the slope is 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 the value of x (60) into the cost function:

C(60) = 570 * 60 + 310
C(60) = 34,200 + 310
C(60) = 34,510

Therefore, the estimated cost to manufacture 60 Xboxes is $34,510.

To obtain the corresponding linear cost function, we can use the formula for the equation of a straight line (y = mx + b), where x represents the number of Xbox 360s and y represents the cost.

First, let's find the slope (m) using the given data:
m = (change in y) / (change in x) = (8290 - 4300) / (14 - 7) = 3990 / 7 = 570.

Now, we can use the slope-intercept form of a linear equation (y = mx + b) to find the y-intercept (b). We can substitute the values of x and y from one of the given data points (e.g., $4300 for 7 Xbox 360s):

4300 = 570(7) + b
4300 = 3990 + b
b = 4300 - 3990 = 310.

Therefore, the linear cost function for manufacturing Xbox 360s is:
C(x) = 570x + 310.

To find the cost to manufacture each additional Xbox, you can calculate the marginal cost by finding the slope of the cost function, which is the coefficient of x (570 in this case). Therefore, the cost to manufacture each additional Xbox is $570.

To estimate the cost of manufacturing 60 Xboxes using the cost function, you can substitute the value of x in the equation:

C(60) = 570(60) + 310
C(60) = 34200 + 310
C(60) = $34,510.

Therefore, the estimated cost to manufacture 60 Xboxes is $34,510.