Answer to Question #205378 in Calculus for Akhona Klanisi

Question

11

The marginal labour cost function is given by the equation

MLC = 3 + 4L.

Calculate the cost of employing the first eight labourers.

a.       −114

b.       114

c.       152

d.       119

 

12

If the demand function is

P = Q² − 7Q − 8,

where P and Q are the price and quantity respectively, determine the point price elasticity of demand (rounded to three decimal places) if P = 51. Is demand elastic or inelastic at this price?

[a.   e_d = −0.075;inelastic [b.  e_d = −0.255;inelastic

[c.   e_d = 1.300; elastic

[d.  e_d = −0.253; inelastic 

Answer 1

Solution.

1.

$MLC=3+4L$

$C=\int\limits_0^8 (3+4L)dL=\newline 3L+2L^2|_0^8=3•8+2•64=24+128=152.$

Answer. c.152

2.

$P=Q^2-7Q-8$

If P=51, then $Q^2-7Q-59=0.$

From here $Q=-4.941,$ or $Q=11.941.$

Find $e_d$ for formula:

$e_d=\frac{dQ}{dP}\frac{P}{Q}$

Find P(Q):

$Q^2-7Q-8-P=0$

$D=49-4(-8-P)=81+4P$

$Q=\frac{7\pm\sqrt{81+4P}}{2}$

$e_d=\pm\frac{1}{\sqrt{81+4P}}\frac{51}{11.941}=\pm 0.253$

$|e_d|<1,$ then demand inelastic.

Answer. d.-0.253, inelastic.