A cost function c(x) for producing x number of units: c(x) =20x+150
c) sketch the cost function c(x) from x=0 to x=50
d) how much will the cost function change if the number of units produced is increased by 6 units
this just a line, with slope=20
so, if x grows by 6, c(x) must grow by 20*6=120
c) To sketch the cost function c(x) from x=0 to x=50, we need to plot the points on a graph. We will calculate the cost for different values of x within the given range.
When x = 0, the cost c(x) = 20(0) + 150 = 150.
When x = 1, the cost c(x) = 20(1) + 150 = 170.
When x = 2, the cost c(x) = 20(2) + 150 = 190.
And so on...
We can calculate the cost for all values of x from 0 to 50 and then plot them on a graph. The x-axis represents the number of units produced (x), and the y-axis represents the cost (c(x)).
d) To find how much the cost function will change if the number of units produced is increased by 6 units, we need to calculate c(x+6) - c(x).
Let's substitute x+6 into the cost function c(x) to find c(x+6):
c(x+6) = 20(x+6) + 150
c(x+6) = 20x + 120 + 150
c(x+6) = 20x + 270
Now, we calculate c(x+6) - c(x):
c(x+6) - c(x) = (20x + 270) - (20x + 150)
c(x+6) - c(x) = 20x + 270 - 20x - 150
c(x+6) - c(x) = 120
Therefore, the cost function will change by 120 units if the number of units produced is increased by 6 units.
To sketch the cost function c(x) from x=0 to x=50, we first need to determine the values of c(x) for each value of x within that range.
Given the cost function c(x) = 20x + 150, we can substitute values of x ranging from 0 to 50 to find the corresponding cost.
For x = 0:
c(0) = 20(0) + 150 = 150
For x = 1:
c(1) = 20(1) + 150 = 170
For x = 2:
c(2) = 20(2) + 150 = 190
Continuing this process, we can find the cost for each value of x within the specified range.
Once we have the values of c(x) for different x values, we can plot them on a graph with x on the horizontal axis and c(x) on the vertical axis. Each point on the graph represents the number of units produced (x) and the corresponding cost (c(x)).
To determine the change in the cost function if the number of units produced is increased by 6 units, we need to calculate the difference between the costs for the initial number of units and the number of units increased by 6.
For example, let's say the initial number of units produced is x, and we want to find the change in cost if the number of units is increased by 6. The new number of units produced would be x + 6.
The initial cost (c(x)) can be calculated using the cost function c(x) = 20x + 150, and the cost for the increased number of units (c(x + 6)) can be calculated by substituting x + 6 into the cost function.
The change in the cost function is then given by:
c(x + 6) - c(x)
By substituting the appropriate values into this expression, you can find the exact change in the cost function if the number of units produced is increased by 6 units.