As the number of units manufactured increases from 4000 to 6000 the total cost of production increases from 22000 to 30000. Assuming a linear relationship between the cost when 4500 units are produced.

if y=cost and x=units, then

y = 4000 + (30-22)/(6-4) x

i don't understand

To find the linear relationship between the number of units produced and the cost, we can use the formula for a straight line:

y = mx + b

Where:
- y is the cost of production
- x is the number of units manufactured
- m is the slope of the line
- b is the y-intercept

Let's find the slope (m) first:

Change in y = 30000 - 22000 = 8000
Change in x = 6000 - 4000 = 2000

m = (Change in y) / (Change in x) = 8000 / 2000 = 4

Now, let's find the value of b by substituting the values of x and y at any point on the line (4500 units produced):

y = mx + b
22000 = 4 * 4000 + b
22000 = 16000 + b
b = 6000

Therefore, the linear relationship between the cost (y) and the number of units manufactured (x) is:

y = 4x + 6000

To determine the cost when 4500 units are produced, we need to find the equation of the linear relationship between the number of units produced and the total cost of production.

We are given two data points: (4000, 22000) and (6000, 30000). Using these points, we can find the equation of the line using the slope-intercept form, y = mx + b, where y is the total cost, x is the number of units produced, m is the slope, and b is the y-intercept.

First, let's calculate the slope:

m = (y2 - y1) / (x2 - x1)
= (30000 - 22000) / (6000 - 4000)
= 8000 / 2000
= 4

Now, let's substitute one of the data points into the slope-intercept form to find the y-intercept (b). Let's use the point (4000, 22000):

22000 = 4(4000) + b
22000 = 16000 + b
b = 22000 - 16000
b = 6000

Therefore, the equation of the linear relationship between the number of units produced (x) and the total cost of production (y) is:

y = 4x + 6000

Now, we can find the cost when 4500 units are produced by substituting the value x = 4500 into the equation:

y = 4(4500) + 6000
= 18000 + 6000
= 24000

Therefore, the cost when 4500 units are produced is 24000.