Question

An industrial production process costs C(q) million dollars to produce q million units; these units then sell for R(q) million dollars.

If C(2.1)=5.1 , R(2.1)=6.6 , MC(2.1)=0.4 and MR(2.1)=0.5, calculate the following.

(a) The profit earned by producing 2.1 million units.

(b) The approximate change in revenue if production increases from 2.1 to 2.14 million units.

(c) The approximate change in revenue if production decreases from 2.1 to 2.07 million units.

(d) The approximate change in profit in parts (b) and (c).

Answer 1

I am assuming MC and MR means Marginal Cost and Marginal Revenue respectively

Answer 2

yes it does.

Answer 3

a)Profit(2.1)= Revenue(2.1)-Cost(2.1)
= 6.6-5.1=1.5

Answer 4

b)Use linearization
L(x) =F'(x)dx+F(x)
R(2.14)=MR(2.1)(0.04)+R(2.1)
0.4*0.04 + 6.6=6.616

Answer 5

what is linearization?

Answer 6

b)Use linearization
L(x) =F'(x)dx+F(x)
R(2.14)=MR(2.1)(0.04)+R(2.1)
0.4*(-0.03) + 6.6=6.588

Answer 7

Linearization means you are approximating something when you know its derivative

Answer 8

I'm not sure I understand the concept, I'm sorry.

Answer 9

Okay, this is detours, to understand the concept of linearization
Say for example, you want to know Square root of 9.2 without calculator,you may use linearization to approximate.
f(x)=Sqrt[x]
f'(x)= 1/2 x^-1/2
We don't know what square root of 9.2 is but we know square root of 9 is 3
f(9.2) = f(9)+f'(9)(.2)
f(9.2) 3 +1/6 (.2)=3.0333

Answer 10

ohh, okay, I understand. So I will linearize for the whole problem?

Answer 11

yep, I hope it makes sense

Answer 12

This is basically we did for b) and c)

Answer 13

so for c, I subtract instead of add.

Answer 14

the number we multiply is negative
\[0.4*\underline{(-0.03)} + 6.6=6.588\]

Answer 15

Do you know how I got 0.03 ?

Answer 16

where did you get that from?

Answer 17

if production decreases from 2.1 to 2.07 million units.

2.1-2.07=.03
negative because we decrease

Answer 18

oh oh makes sense, I missed that. Okay so then for the last part, I average b and c together, right?

Answer 19

but why did we get 6.6 and 6.588?

Answer 20

so to get jusssssssssssssst the change, i only multiply?so for d, i average them?

Answer 21

They want the CHANGE in profit.
profit=reveune - cost
dp= dr-dc

You know dr, you don't know dc(change in cost),tying to find that for b)

Answer 22

I don't understand:x

Answer 23

Okay, hold on MR dx
b) change in revenue= 0.5*0.04= 0.02
c) change in revenue= 0.5*(-0.03)=-0.015
I incorrectly use MC instead of MR above

Answer 24

Let's do d)

We want change in cost for b)
MC * dx
0.4*0.04 =0.016
c)
0.4 -.03=-0.012

Answer 25

Remember Profit= Revenue - Cost

To get change in Profit= Change in Rev - Change in Cost
for b) 0.02 - 0.016=0.004
for c) -0.015 - -0.012=-0.003

Answer 26

so 0.02 in b would be what in dollars though?

Answer 27

change in revenue in b 0.02 million would be $20,000

Answer 28

I'm trying to understand d.

Answer 29

What doesn't make sense?

Answer 30

the change in cost part

Answer 31

It is same as what we did with revenue but we used MC instead of MR

Answer 32

oh okay! I think i get it:)

Answer 33

so .004 would be 4000 dollars right? so hypothetically, .024 would be 24000?

Answer 34

wait what?

Answer 35

You multiply by a million

Answer 36

I got everything right except d:x

Answer 37

did you put for 4000, -3000 for d?

Answer 38

it like reversed values.

Answer 39

you means it was -3000 and 40000

Answer 40

and then when I plugged in values for the next problem, I got the same thing, everything right except d.

Answer 41

Can you check to see if this value for d is right
$18400,-13800

Answer 42

unfortunately if i get the problem wrong, it gives me another:x

Answer 43

I see, Post you question, I will try to solve it; If I am right, I will explains how I did it

Answer 44

An industrial production process costs C(q) million dollars to produce q million units; these units then sell for R(q) million dollars.

If C(2.1)=5.4 R(2.1)=6.5, MC(2.1)=0.3and MR(2.1)=0.4 calculate the following.

(a) The profit earned by producing 2.1 million units.

(b) The approximate change in revenue if production increases from 2.1 to 2.12million units.

(c) The approximate change in revenue if production decreases from 2.1 to 2.03million units.

(d) The approximate change in profit in parts (b) and (c).

Answer 45

a)1.1
b)0.008
c)-0.028
d) 0.001,-0.008

Answer 46

i got 2000 and -7000 for d

Answer 47

Try my answer

Answer 48

still wrong, but I got the next one right:) you subtract by change in cost then convert to thousand dollars

Answer 49

thankyou for all your help!:) i appreciate it!