The total cost of x units of output of a firm is given by C = `2/3x + 35/2`. Find the

- cost when output is 4 units
- average cost when output is 10 units
- marginal cost when output is 3 units

#### Solution

C = `2/3x + 35/2`

i.e., C(x) = `2/3 x + 35/2`

**(i)** Cost when output is 4 units, i.e., to find when x = 4, C = ?

C(4) = `2/3(4) + 35/2`

C = `8/3 + 35/2`

C = `(8 xx 2 + 35 xx 3)/(3 xx 2) = (16 + 105)/6`

= ₹ `121/6`

**(ii)** Average cost when output is 10 units, i.e., to find when x = 10, AC = ?

C = `2/3 x + 35/2`

Average Cost (AC) = `"Total cost"/"Output" = ("C"(x))/x = ("f"(x) + k)/x`

`= (2/3 x + 35/2)/x = 2/3 x/x + 35/2 1/x`

AC = `2/3 + 35/2 xx 1/x`

When x = 10, AC = `2/3 + 35/2 xx 1/10`

`= 2/3 + 7/2 xx 1/2 = 2/3 + 7/4`

`= (2 xx 4 + 7xx3)/(3 xx 4)`

`= (8 + 21)/12`

`= 29/12`

Average cost when output is 10 units is ₹ `29/12`

**(iii)** Marginal cost when output is 3 units

C = `2/3x + 35/2`

Marginal Cost (MC) = `"d"/"dx"`(C)

`= "d"/"dx" (2/3x + 35/2)`

`= 2/3 "d"/"dx" (x) + "d"/"dx" (35/2)`

`= 2/3 (1) + 0 = 2/3`

Marginal cost when output is 3 units will be ₹ `2/3`