q 0 50 100 150 200 250 300
C'(q) 22 24 23 31 29 31 37
a) If the fixed cost is $11400, use the average of left- and right-hand sums to determine the total cost of producing 150 units.
Answer: $
How much would the total cost increase if production were increased one unit, to 151 units?

Question

q	0	50	100	150	200	250	300
C'(q)	22	24	23	31	29	31	37
a) If the fixed cost is $11400, use the average of left- and right-hand sums to determine the total cost of producing 150 units.
Answer: $
How much would the total cost increase if production were increased one unit, to 151 units?

pulsified333 · Answer

@zepdrix

pulsified333 · Answer

@ganeshie8

ganeshie8 · Answer

$$C(q)-C(0) ~~=~~ \int\limits_0^q C'(q)\,dq$$

ganeshie8 · Answer

It is given that fixed cost is $11400
so, $C(0) = 11400$ : 

$$C(q)-11400~~=~~ \int\limits_0^q C'(q)\,dq$$

ganeshie8 · Answer

You can evaluate the right hand side from the given table. Do you know how to approximate the integral when a table is given ?

pulsified333 · Answer

yes i found the average of the right and left hand sum which is 5625

pulsified333 · Answer

@ganeshie8

ganeshie8 · Answer

I'm getting a different number, can you show ur work how you got 5625

pulsified333 · Answer

Left hand sum= 50(22+24+23)=3450
Right hand sum=50(31+23+24)=3900
And you take the average of the two which is 5625

pulsified333 · Answer

is that right?

ganeshie8 · Answer

first two lines are correct
third line is wrong

ganeshie8 · Answer

how can average of 3450 and 3900 be 5625 ?

pulsified333 · Answer

damn i just realized that. For some reason my calculations are off

pulsified333 · Answer

it should be 3,675

pulsified333 · Answer

@ganeshie8

ganeshie8 · Answer

Yes

pulsified333 · Answer

Im just not sure how to incorporate the fix cost

ganeshie8 · Answer

fixed is the cost when the number of items is 0 : 

C(0) is the fixed cost

ganeshie8 · Answer

$$C(q)-11400~~=~~ \int\limits_0^q C'(q)\,dq$$

$$C(150)-11400~~=~~ \int\limits_0^{150} C'(q)\,dq\approx 3675$$

ganeshie8 · Answer

$$C(150) - 11400 = 3675$$

solve $C(150)$

pulsified333 · Answer

Oh okay

pulsified333 · Answer

C(150)=15,075

pulsified333 · Answer

@ganeshie8 how do you find the second part?

ganeshie8 · Answer

use the tangent approximation

ganeshie8 · Answer

f(x+1) = f(x) + f'(x)*1 = f(x) + f'(x)

ganeshie8 · Answer

C(150+1) = C(150) + C'(150)

ganeshie8 · Answer

you have just worked the value of C(150)

and you can lookup C'(150) from the given table

pulsified333 · Answer

31+15075?

ganeshie8 · Answer

Yep!

pulsified333 · Answer

it says its wrong

pulsified333 · Answer

oh never mind i got it because it was asking for the amount it increased which was 31:D