$3.$ The Bramwell Corporation has estimated its demand function and total cost function to be$$

as follows:

Q $=25-0\mathrm{.}05$P

TC $=700+200$Q

$$Answer the following questions either by developing demand and cost schedules $($Hint: Use$$

quantities from $1$ to $14)$ or by solving the equations.

a$.$ What will be the price and quantity if Bramwell wants to

$1.$ Maximize profits?

$2.$ Maximize revenue?

$3.$ Maximize revenue but require the profit to be a minimum of $$300?$

b$.$ Now assume the cost function is TC $=780+200$Q$,$ while the demand function remains$$

the same. What will the price and quantity be if Bramwell wants to

$1.$ Maximize profits?

$2.$ Maximize revenue?

$3.$ Maximize revenue but require the profit to be a minimum of $$300?$

c$.$ Why are the answers the same in a$(1)$ and b$(1)$ but different in a$(3)$ and b$(3)?$