The price p and the quantity x sold of a small flat-screen television set obeys the demand equation below.

a) How much should be charged for the television set if there are 70

television sets in stock?

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