The Physics Club sells Emc2 T-shirts at the local flea market. Unfortunately, th
ID: 2889568 • Letter: T
Question
The Physics Club sells Emc2 T-shirts at the local flea market. Unfortunately, the club's previous administration has been losing money for years, so you decide to do an analysis of the sales. A quadratic regression based on old sales data reveals the following demand equation for the T-shirts: q =-2p2 + 33p (98 p 15). Here, p is the price the club charges per T-shirt, and q is the number it can sell each day at the flea market (a) obtain a form ula for the price elasticity of demand for E = mc2 T-shirts. (b) Compute the elasticity of demand if the price is set at $10 per shirt. (Round your answer to two decimal places.) Interpret the result. The demand for E me2 T-shirts is going by about 96 per 1% increase in the price (c) How much should the Physics Club charge for the T-shirts in order to obtain the maximum daily revenue? What will the revenue be?Explanation / Answer
given q=-2p2+33p
dq/dp=-2*2p2-1+33*1
dq/dp=-4p+33
(a)
price elasticity of demand,E=(dq/dp)*(p/q)
price elasticity of demand ,E=(-4p+33)*(p/(-2p2+33p))
price elasticity of demand ,E=((-4p+33)p)/((-2p+33)p)
price elasticity of demand ,E=(-4p+33)/(-2p+33)
(b)
p =10 when price is $ per shirt
price elasticity of demand ,E=(-4*10 +33)/(-2*10 +33)
price elasticity of demand ,E=(-40 +33)/(-20 +33)
price elasticity of demand ,E=-7/13
price elasticity of demand ,E= -0.54
the demand for E=mc2 T-shirts is going down by about 0.54 % per 1% increases in the price
(c)
for maximum revenue ,|E|=1
=>|(-4p+33)/(-2p+33)|=1
=>(-4p+33)/(-2p+33)=-1 ,(-4p+33)/(-2p+33) =1
=>-4p+33 =2p-33 , -4p+33 =-2p+33
=>2p+4p=33+33 , p=0
=>6p =66
=>p=11
physics club should charge $11 per shirt to maximise revenue
revenue =11*(-2*112 +33*11)
revenue = 1331
revenue will be $ 1331
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