The demand function for a product is modeled by p = 400 − 4x, 0 ≤ x ≤ 100, where p is the price per unit (in dollars) and x is the number of units. (a) Determine when the demand is elastic and inelastic. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

Demand is Elastic when Price > 200 ; Demand is inelastic when Price < 200

Step-by-step explanation:

p = 400 - 4x

4x = 400 - p

x = (400 - p) / 4 → x = 100 - p/4

Elasticity of demand  [ P ed ] = (Δx / Δp) x (p / x)

Δx / Δp  [Differentiating x w.r.t p]  = 0 - 1/4  → = -1/4

P ed =  -1 x p

            4   (400 - p)/4

= -1 x 4p              = -p / (400-p)

  4   (400 - p)

Price Elasticity of demand : only magnitude is considered, negative sign is ignored (due to negative price demand relationship as per law of demand).

So, Ped = p / (400 - p)

Demand is Elastic when P.ed > 1

p / (400-p)  > 1

p > 400 - p

p + p > 400  → 2p > 400

p > 400 / 2 →  p > 200

Demand is inelastic when P.ed < 1

p / (400-p)  < 1

p < 400 - p

p + p < 400  → 2p < 400

p < 400 / 2 →  p < 200

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