Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# Revenue function ‘R’ and cost function ‘C’ are R = 14x – x2 and C = x(x2 – 2). Find the 1. average cost 2. marginal cost 3. average revenue and 4. marginal revenue. - Business Mathematics and Statistics

Sum

Revenue function ‘R’ and cost function ‘C’ are R = 14x – x2 and C = x(x2 – 2). Find the

1. average cost
2. marginal cost
3. average revenue and
4. marginal revenue.

#### Solution

R = 14x – x2 and C = x(x2 – 2)

C = x3 – 2x

(i) Average Cost (AC) = "Total cost"/"Output" = ("C"(x))/x

= (x^3 - 2x)/x

= x^3/x - (2x)/x

= x2 – 2

(ii) Marginal Cost (MC) = "dC"/"dx"

= "d"/"dx" (x^3 - 2x)

= "d"/"dx" (x^3) - 2 "d"/"dx" (x)

= 3x2 – 2

(iii) Average Revenue R = 14x – x2

Average Revenue (AR) ="Total Revenue"/"Output" = ("R"(x))/x

= (14x - x^2)/x

= (14x)/x - x^2/x

= 14 - x

(iv) Marginal Revenue (MR) = "dR"/"dx"

= "d"/"dx" (14x - x^2)

= 14 "d"/"dx" (x) - "d"/"dx" (x^2)

= 14(1) – 2x

= 14 – 2x

Concept: Applications of Differentiation in Business and Economics
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