- Ian HLv 74 weeks ago
Quantity demanded in units per period, (for example daily sales) represented by Q
The variable representing price is p, so the demand function is
Sales Q = 150 – 10p, where p is price
Revenue R is price per item * number sold
R = p*Q = 150p – 10p^2
a) To find maximum R, differentiate and set that result equal to zero.
dR/dp = 150 – 20p = 0
Revenue R is at a max when price p = 7.5
Sales Q when total revenue is at its max is given by Q = 150 – 75 = 75
b) The question repeats “find price at which total revenue is a max”
It seems likely that this should have asked for that max revenue.
If so, R max = 150*7.5 – 10*7.5^2 = 562.5