Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# Find the marginal productivities of capital (K) and labour (L) if P = 8L – 2K + 3K2 – 2L2 + 7KL when K = 3 and L = 1. - Business Mathematics and Statistics

Sum

Find the marginal productivities of capital (K) and labour (L) if P = 8L – 2K + 3K2 – 2L2 + 7KL when K = 3 and L = 1.

#### Solution

P = 8L – 2K + 3K2 – 2L2 + 7KL

Marginal productivity of labour, (del"P")/(del"L") = 8 – 0 + 0 – 2(2L) + 7K(1)

= 8 – 4L + 7K

Marginal productivity of labour when K = 3 and L = 1 is

((del"P")/(del"L"))_((3;1)) = 8 – 4 + 21

= 29 – 4

= 25

Marginal productivity of capital, (del"P")/(del"K") = 0 – 2(1) + 3(2K) – 0 + 7L(1)

= -2 + 6K + 7L

Marginal productivity of capital when K = 3 and L = 1 is

((del"P")/(del"K"))_((3;1))

= -2 + 18 + 7

= -2 + 25

= 23

Concept: Applications of Partial Derivatives
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Business Mathematics and Statistics Answers Guide
Chapter 6 Applications of Differentiation
Exercise 6.5 | Q 1 | Page 154
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