Answer:
The correct answer is NO. The best price to be charged is $3.75
Step-by-step explanation:
Demand equation is given by Q = 30 - 4P, where Q is the quantity of necklaces demanded and P is the price of the necklace.
⇒ 4P = 30 - Q
⇒ P = [tex]\frac{30-Q}{4}[/tex]
The current price of the necklace $10.
Revenue function is given by R = P × Q = [tex]\frac{1}{4}[/tex] × ( 30Q - [tex]Q^{2}[/tex])
To maximize the revenue function we differentiate the function with respect to Q and equate it to zero.
[tex]\frac{dR}{dQ}[/tex] = [tex]\frac{1}{4}[/tex] × ( 30 - 2Q) = 0
⇒ Q = 15.
The second order derivative is negative showing that the value of Q is maximum.
Therefore P at Q = 15 is $3.75.
Thus to maximize revenue the price should be $3.75.
The price of $10 per necklace is not the best price to charge in order to maximize revenues
The demand equation is given as:
[tex]Q=30 - 4P[/tex]
The price is given as:
P = 10
Substitute 10 for P in the demand equation
[tex]Q=30 - 4 \times 10[/tex]
Multiply 4 by 10
[tex]Q=30 - 40[/tex]
Subtract 40 from 30
[tex]Q = -10[/tex]
A negative value of the quantity (Q) means that, the price of $10 per necklace is not the best price
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