Answer with Step-by-step explanation:
We are given that a demand function
[tex]x=D(p)=3100-20p[/tex]
Where x=The quantity of sodas sold
p=Per can price (in cents)
We have to find the price p for which the demand inelastic.
Differentiate the demand function w.r.t p
[tex]D'(P)=-20[/tex]
Price elasticity of demand=[tex]E(p)=\frac{-pD'(p)}{D(p)}[/tex]
Price elasticity of demand=[tex]E(p)=\frac{-p(-20)}{3100-20p}[/tex]
When demand is inelastic then
E(p)<1
[tex]\frac{20p}{3100-20p}[/tex] <1
Multiply by (3100-20p) on both sides
[tex]20p<3100-20p[/tex]
Adding 20p on both side of inequality
[tex]40p<3100[/tex]
Divide by 40 on both sides
[tex]p<77.5[/tex]
When the value of price is less than 77.5 then the demand of elasticity is inelastic.
