A cost function c(x) for producing x number of units: c(x) =20x+150
a) what would be the cost of producing 10 units
b) how many units would have to be produced to cost 750
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
(a) c(10)= 20 (10)+150 = 350
(b) 20(x) +150=750
x=(750-150)/20
=30
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what happened to question c and question d
To answer these questions, we will need to substitute x with the given values in the cost function c(x) = 20x + 150.
a) To find the cost of producing 10 units, substitute x = 10 into the cost function:
c(10) = 20*10 + 150
= 200 + 150
= 350
Therefore, the cost of producing 10 units would be $350.
b) To find the number of units that would cost $750, substitute c(x) = 750 into the cost function:
750 = 20x + 150
Subtract 150 from both sides:
600 = 20x
Divide both sides by 20:
x = 600/20
x = 30
Therefore, to cost $750, you would need to produce 30 units.
c) To sketch the cost function c(x) from x = 0 to x = 50, we need to plot the points for different x values in this range. So, we can choose some x values and calculate the corresponding cost values using the cost function. For example, let's consider x = 0, 10, 20, 30, 40, and 50:
For x = 0:
c(0) = 20*0 + 150
= 150
For x = 10:
c(10) = 20*10 + 150
= 200 + 150
= 350
For x = 20:
c(20) = 20*20 + 150
= 400 + 150
= 550
For x = 30:
c(30) = 20*30 + 150
= 600 + 150
= 750
For x = 40:
c(40) = 20*40 + 150
= 800 + 150
= 950
For x = 50:
c(50) = 20*50 + 150
= 1000 + 150
= 1150
Now, plot these x and c(x) values on a graph with x on the horizontal axis and c(x) on the vertical axis. Connect the points to get a smooth curve. This will represent the cost function graph from x = 0 to x = 50.
d) To find out how much the cost function will change if the number of units produced is increased by 6 units, we need to calculate the difference between the cost function for the new number of units and the previous number of units.
Let's say the original number of units is x, then the new number of units is x + 6.
The change in cost function = c(x + 6) - c(x)
= (20 * (x + 6) + 150) - (20 * x + 150)
= (20x + 120 + 150) - (20x + 150)
= 20x + 270 - 20x - 150
= 120
Therefore, the cost function will change by $120 if the number of units produced is increased by 6 units.