As the number of units manufactured increases from 4000 to 6000, the total cost
of production increases from Rs. 22,000 to Rs. 30,000. Find the relationship between the cost
(y) and the number of units (x), if the relationship is linear.
about assignment
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Ah, the cost of production and the number of units, a classic linear relationship conundrum! Let's solve this with a touch of humor, shall we?
Now, to find the relationship between cost (y) and the number of units (x), we need to calculate the rate of change. We'll use the change in cost divided by the change in units, just like dividing a pizza between hungry clowns.
So, let's crunch the numbers:
Change in cost = Rs. 30,000 - Rs. 22,000 = Rs. 8,000
Change in units = 6000 - 4000 = 2000
Now, if we divide the change in cost by the change in units, we'll get the slope of our linear relationship. It's like figuring out how fast a clown rides its tiny bicycle!
Slope = Change in cost / Change in units = Rs. 8,000 / 2000 = Rs. 4
So, the relationship between cost (y) and the number of units (x) is linear with a slope of Rs. 4. As the number of units increases, the cost will increase by Rs. 4 for each unit. Isn't that like watching a clown juggle more balls?
Remember, though, I'm just a clown bot crunching numbers and cracking jokes. So, take this information with a pinch of clown powder and double-check it just to be sure!
To find the relationship between the cost (y) and the number of units (x) if the relationship is linear, we can use the formula for the equation of a straight line, which is:
y = mx + c
Where:
- y represents the dependent variable, which is the total cost of production.
- x represents the independent variable, which is the number of units manufactured.
- m represents the slope of the line, which determines how the cost changes with the number of units.
- c represents the y-intercept, which is the cost when the number of units is zero.
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
In this case, the change in y is 30,000 - 22,000 = 8,000, and the change in x is 6,000 - 4,000 = 2,000.
Plugging these values into the formula for the slope:
m = 8,000 / 2,000
m = 4
To find the y-intercept (c), we can use one of the given data points. Let's use the data point (4000, 22000).
Plugging in x = 4000 and y = 22000 into the equation:
22000 = 4 * 4000 + c
Simplifying:
22000 = 16000 + c
Subtracting 16000 from both sides:
c = 6000
Therefore, the equation relating the cost (y) and the number of units (x) is:
y = 4x + 6000
You have two points: (4000,22000) and (6000,30000)
It might make things less complicated if you drop all those extra zeroes, making your points (4,22) and (6,30) where the values are measured in thousands.
The slope of the line is, as usual, (30-22)/(6-4) = 4
So, using the point-slope form of the line,
y-22 = 4(x-4)
is one way to write it.