The price p and quantity x sold of a small flat screen television set obeys the demand equation below.
p= - .14x+280
:
a. How much should be charged for the television set if there are 60 television sets in stock? Round to nearest cent
p = -.14(60) + 280
p = -8.4 + 280
p = $271.60
:
b. What quantity x will maximize revenue?
Rev = qty * price
R(x) = x(-.14x+280)
R(x) -.14x^2 + 280x
The axis of symmetry is the qty for max revenue;x = -b/(2a)
x =
x = + 1000 tv's for max rev
:
What is the maximum revenue?
rev = -.14(1000^2) + 280(1000)
rev = -140000 + 280000
rev = $140,000
:
:
c. What price should be charged in order to maximize revenue?
p = -.14x + 280
p = -.14(1000) + 280
p = -140 + 280
p = $140
