A quadratic regression based on old sales data reveals the following demand equation for the T-shirts:
q = −2p^2 + 24p (9 ≤ 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 formula for the price elasticity of demand for E = mc2 T-shirts.
(b) Compute the elasticity of demand if the price is set at $15 per shirt.
(c) How much should the Physics Club charge for the T-shirts in order to obtain the maximum daily revenue?
(d)What will the revenue be?
q = −2p^2 + 24p (9 ≤ 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 formula for the price elasticity of demand for E = mc2 T-shirts.
(b) Compute the elasticity of demand if the price is set at $15 per shirt.
(c) How much should the Physics Club charge for the T-shirts in order to obtain the maximum daily revenue?
(d)What will the revenue be?
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q = −2p^2 + 24p (9 ≤ p ≤ 15)
E = -(p/q)dq/dp = -[(-4p + 24)][p/(-2p² + 24p)] = (12- 2p)/(p - 12)
p = 15 ==> E = - 6 ===> inelastic
max revenue for E = 1
==> 12- 2p = p - 12 ==> p = 8
q(8) = 64
E = -(p/q)dq/dp = -[(-4p + 24)][p/(-2p² + 24p)] = (12- 2p)/(p - 12)
p = 15 ==> E = - 6 ===> inelastic
max revenue for E = 1
==> 12- 2p = p - 12 ==> p = 8
q(8) = 64