I really need help with this economics, can someone see if i did this right?

demand function P=2,000-50Q
a) to sell 20 units of Q, what price would have to be charged?

is this P=1000?

b) if firm sets a price of $500, how many units of Q would be sold


c) what is the price elasticity of demand if price equals $500

d) at what price if any, will the demand of Q be unitary elastic
this one i just dont know how to do

any help would be greatly appreciated

a and b are correct

c price elasticity equals change in Q divided by change in P

at $500 Q is 30, at $450 Q is 31
1/30 = change Q
50/500 = change P

d) I had to plot in a lot of quantities and prices. Knowing that total revenue would be at the maximum when unitary elastic. I calculated
15Q x $1,250p = $18,750
20Q x $2,000p = $20,000
25Q x $750p = $1,8750
So maximum is 20 Q calculate elasticity and it is = 1

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