Question

1. Recall that the elasticity of demand is defined by

E(p) = −pf0 (p) f(p) (

a) Let the demand equation for hand sanitizer be given by f(p) = p 20 − p 2 Find E(p) and then compute E(4).

(b) If E(p) = 1.5, interpret what this would mean for the selling of hand sanitizers.

2. Suppose the demand of mathematical textbooks is given by the equation d(x) = x 2 + 6x + 2

(a) State the revenue function

(b) Find the marginal revenue.

3. A 20f t ladder leaning against a wall begins to slide. How fast is the top of the ladder at the instant of time when the bottom of the ladder is 12f t from the wall and sliding away from the wall at the rate of 5f t per second?

Wall 20-ft ladder 5 ft/sec

Answer 1

the a) F(p) = 20p- p² EIP = dflP) x 1 dp f(p) DFID) - 20-22 ap ELP) - - 120-2p) x P. 20p-p2 E(4)= - (20-214)) x 4 2014)-14) - - (20-8) x 4 so-16 = - (12) x 4 | E(4) = - 0.75

Aus d(x) = x² + 6 x + 2 a) Revenue function Ruunu - dead.x = x² + 6x² + 20 b) Marginal runnur MR= d Reunu - 3 x ² +124t2 dx АҚ, go ft x= 12ft sec with we have dx = 5A x and y are related by pythagorean throum x² + y² = (2012 Dipper Hating both the ides 2x dx & 24 dy = 0 dy - – 2 de It y at why - 12 P y = J 90)² – (12) 2 . | Yoo - 144 = 25 y = 14

Therefore, dy = -2 *5 158 4 sec