3-4-23 average cost
X
00:00
/
00:00
CC
Suppose that the dollar cost of producing X appliances is C of X
equal 500 + 1 twenty X -, .2 X squared.
We want to find the average cost per appliance of producing the
1st 130 appliances.
So to find the cost of the 1st 130 appliances, we're just going
to put 130 in to the C of X.
But if we want the average, we're going to take the total
amount to produce 130 and we're going to divide it by 130.
That's going to be the average cost per appliance if we're
making 130 of them.
So putting that in dividing, we get approximately 97.85.
The second one says find the marginal cost when 130
appliances are produced.
So the marginal cost is going to be that derivative.
So we're going to figure out what the derivative is 120 -, .4
X and then we're going to put in the 130 into that equation.
So the marginal cost is $68, show that the marginal cost when
130 appliances are produced is approximately the cost of
producing one more appliance after the 1st 130 have been made
by calculating the latter cost directly.
So what we're really doing on this last one is we're finding
the slope and we're taking 131 -, 130 for the cost divided by
131 -, 130, which is understood to be a one.
So the cost of 131 appliances minus the cost of 130 appliances
all divided by one is 67.8.