Question

Find the values of Total Cost and Average Cost at x = 3 and 8, if the total
cost functions is C = 5 + 4x + 2x2 *​

Answer 1

Answer:

We have,

C(x)=x2+75x+1600

Cˉ(x)=xC(x)

Cˉ(x)=xx2+75x+1600

Cˉ(x)=x+75+x1600

Now,

C′ˉ(x)=dxdCˉ(x)

=1−x21600

For the minimum average cost C′(x)=0

1−x21600=0

x=40

Now,

C"ˉ(x)=dx2d2C(x)

So, x33200>0 [for x=40]

Therefore, it is minimum.

Therefore, the minimum average cost

Cˉ(x)=40+75+

Answer 2

We have,

C(x)=x

2

+75x+1600

C

ˉ

(x)=

x

C(x)

C

ˉ

(x)=

x

x

2

+75x+1600

C

ˉ

(x)=x+75+

x

1600

Now,

C

′

ˉ

(x)=

dx

d

C

ˉ

(x)

=1−

x

2

1600

For the minimum average cost C

′

(x)=0

1−

x

2

1600

=0

x=40

Now,

C"

ˉ

(x)=

dx

2

d

2

C(x)

So,

x

3

3200

>0 [for x=40]

Therefore, it is minimum.

Therefore, the minimum average cost

C

ˉ

(x)=40+75+

40

1600

=155

Therefore, C

A

=155

Now, we find marginal cost i.e.,

C

m

=

dx

dC

C

m

=

dx

d

(x

2

+75x+1600)

C

m

=2x+75

Put x=40, we get

C−m=2×40+75

C

m

=80+75=155

Thus, C

A

=C

m

for x=40

Hence, this is the answer.