As the number of units manufactured increases from 4000 to 6000 the total cost of production increases form $22000 to $30000. Assuming a linear relationship between the cost and the number of units manufactured, what will be the cost when 4500 units are produced.
everything in thousands
two points on line
(4,22) and (6,30)
(30-22)/(6-4) = slope
so slope = m = 4
c = 4 n + b
22 = 16 + b
b = 6
so
c = 4 n + 6
if n = 4.5
c = 4(4.5) + 6
c = 18+6
c = 24
so
24,000
To find the cost when 4500 units are produced, we can use the equation of a straight line, which is given by y = mx + b, where y is the dependent variable (cost), x is the independent variable (number of units manufactured), m is the slope, and b is the y-intercept.
First, we need to determine the values of m and b. We are given two data points: (4000, 22000) and (6000, 30000).
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the data points:
m = (30000 - 22000) / (6000 - 4000)
= 8000 / 2000
= 4
Now that we have the slope (m), we can determine the y-intercept (b) by substituting one of the data points into the equation:
22000 = 4(4000) + b
Solving for b:
22000 = 16000 + b
b = 22000 - 16000
b = 6000
Therefore, the equation for the relationship between the cost and the number of units manufactured is:
y = 4x + 6000
Now we can substitute x = 4500 into the equation to find the cost:
y = 4(4500) + 6000
y = 18000 + 6000
y = 24000
Therefore, the cost when 4500 units are produced will be $24,000.