Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# The total cost of x units of output of a firm is given by C = 2/3x + 35/2. Find the 1. cost when output is 4 units - Business Mathematics and Statistics

Sum

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

1. cost when output is 4 units
2. average cost when output is 10 units
3. 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

Concept: Applications of Differentiation in Business and Economics
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