The estimated monthly sales of Mona Lisa paint-by-number sets is given by the fo

Question

The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q105ev -3p72, where q is the demand in monthly sales and p is the retail price in (a) Determine the price elasticity of demand E when the retail price is set at 3 yen. Enter an exact number Interpret your answer. The demand is going downby X % per 1% increase in price at that price level. Thus, a large price decrease V is advised. (b) At what price will revenue be a maximum? (Round your answer to two decimal places.) 1/3 X yen (c) Approximately how many paint-by-number sets will be sold per month at the price in part (b)? (Round your answer to the nearest integer.) x paint-by-number sets per month

Explanation / Answer

given,q=105ep-3p2/2

=>dq/dp=105(1-3p)ep-3p2/2

(a)

E=(dq/dp)*(p/q)

E=(105(1-3p)ep-3p2/2)*(p/105ep-3p2/2)

E=(1-3p)p

when price is 3 yen , p=3

E=(1-3*3)*3

=>E=(1-9)*3

=>E=(-8)*3

=>E= -24

|E|=24 >1

the demand is going down by 24% per 1% increase in price at that price level.this a large price decrrease is advised

(b)

revenue is maximum when ,|E|=1

=>|(1-3p)p|=1

=>-3p2+p =-1

=>p2-(1/3)p =(1/3)

=>p2-2(1/6)p +(1/6)2 =(1/6)2+(1/3)

=>(p-(1/6))2 =(13/36)

=>p =(1/6)(1+13)

=>p=0.76759187924399821551987021124508

0.77 yen

(c)

q=105e0.76759187924399821551987021124508-3*0.767591879243998215519870211245082/2

=>q = 71.755

72 paint -by-number sets per month

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