A fried chicken franchise finds that the demand equation for...

A fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by p = 43/ q^1.5 , where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price. Express q as a function of p. q = ______ Find the price elasticity of demand when the price is set at $4.30 per serving. _____ Interpret the result. They should ____ the price per serving in order to increase revenue.

Transcript

00:01 In this problem we are given the demand equation for a new roast chicken given by p equal to 43 divided by q raised to the power 1 .5 where p is the price in dollars per quarter chicken serving and q is the number of quarter chicken servings that can be sold per hour at this price.

00:20 For part a of the problem we have to express q as a function of p.

00:24 So to express q as a function of p we will cross multiply the given equation.

00:30 And it can be written as q raised to the power 1 .5 equal to 43 divided by p now now we will raise both the sides of the equation by a power of 2 divided by 3 so q 1 .5 raised to the power 2 divided by 3 will be equal to 43 divided by p raised to the power 2 divided by 3 now q 1 .5 can be written as 3 divided by 2 and it can be cancelled out with 2 divided by 3 so we will have have q equal to 43 divided by p whole raise to the power 2 divided by 3 this is the answer to the first part of the problem next in part b we have to find the price elasticity of demand when the price is set as set at dollars 4 .30 per circle so here first we will differentiate find the first derivative of q with respect to p that means q dash which is given by d divided by d p of 43 divided by q raised to the power 2 divided by 3 in the next step after derivating we will have q dash equal to 43 raised to the power 2 divided by 3 multiplied by minus 2 divided by 3 p raised to the power minus 5 divided by 3 which also can be written as minus 2 multiplied by 43 raised to the power 2 divided by 3 divided by 3 divided by by 3p ratio of the power 5 divided by 3.

02:10 Now elasticity of demand equation, let's know that by e of p, capital e of p is given by the absolute value of p divided by q of p minus q dash of p multiplied by, sorry, it is multiplied by q dash of p...

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