Question

use c(x)=1/6x^2+3x+42;p(x)=1/5(35-x) where x is the number of units sold, to find the following:
(A) an expression for revenue
(B) the marginal cost and marginal revenue
(C) the marginal cost to produce the 5th unit
(D) the actual cost to produce the 5th unit
(E) the marginal revenue derived from the sale of the 5th unit
(F) the actual revenue derived from the sale of the 5th unit

Answer 1

assuming p(x) is profit, c(x) is cost

Answer 2

yes it is

Answer 3

Profit = revenue - cost

Answer 4

rearranging
revenue = profit + cost

Answer 5

so you take both equations and add them

Answer 6

yes

Answer 7

R(x) = c(x) + p(x)
R(x) = 1/6x^2+3x+42 + 1/5(35-x)

Answer 8

so it would be 1/6 x 2 +2.8x +49

Answer 9

1/30 (5 x^2+84 x+1470)

Answer 10

yes that is correct

Answer 11

my answers wrong?

Answer 12

no, we had equivalent answers

Answer 13

ok b?

Answer 14

marginal cost = C'(x)
marginal revenue = R'(x)

Answer 15

for revenue are we using the equation derivative of marginal cost

Answer 16

the derivative of the function we got

Answer 17

for marginal cost i got .33x+3 and for revenue i got .33

Answer 18

C ' (x) = 1/3 x + 3
R'(x) = 1/3x + 2.8

Answer 19

ok c?

Answer 20

so for c do we plug in 5 for x

Answer 21

one moment, checking

Answer 22

how do you do d

Answer 23

ok

Answer 24

MARGINAL COST
If C( x) is the total cost of producing x units of a commodity, then the marginal cost of
producing xo units is the derivative C′( xo) , which approximates the additional cost
C(xo + 1) - C(xo) incurred when
the level of production is increased by one unit, from xo to xo +1.

Answer 25

so it would be c(5)-c(4)?

Answer 26

ok

Answer 27

so -2.66

Answer 28

3.33

Answer 29

(C) the marginal cost to produce the 5th unit
C'(4)
(D) the actual cost to produce the 5th unit
C(5) - C(4)
(E) the marginal revenue derived from the sale of the 5th unit
(F) the actual revenue derived from the sale of the 5th unit

Answer 30

?

Answer 31

so c is plugging in 4 instead of 5

Answer 32

(C) the marginal cost to produce the 5th unit
c'(4) = 1/3*4 + 3

(D) the actual cost to produce the 5th unit
c(5) - c(4) = (1/6*5^2 + 3*5 +42 ) - (1/6*4^2 + 3*4+42)

Answer 33

so what do we do for e

Answer 34

(E) the marginal revenue derived from the sale of the 5th unit

r'(4) = 1/3*4 + 2.8

(F) the actual revenue derived from the sale of the 5th unit

r(5) - r(4) = (1/6*5^2 +2.8*5 +49) - (1/6*4^2 +2.8*4 +49)

Answer 35

c) 4.33
d) 4.5
e)4.13
f)4.30

Answer 36

thank you

Answer 37

is it correct ?

Answer 38

there might be an arithmetic error, so fingers crossed

Answer 39

yes its correct

Answer 40

wait for f why are we using the revenue equation that we got

Answer 41

because we are asking for the actual change in revenue , to go from the fourth unit to the fifth

Answer 42

so shouldn't d and f be the same answer

Answer 43

d) is actual cost, not revenue

Answer 44

f) is actual revenue

Answer 45

oh

Answer 46

:D

Answer 47

OOOH A MOD

Answer 48

how me become one??