Please help asap

Question

The Demand equation for an item currently being marketed is given by

D(q)= −0.15 ⋅ q^2+ 59, where D(q) is in $ that can be charged per unit, and q is in thousands of units that can be sold at that price. (For example, q=20 means 20,000 units can be sold.) If 9,000 units are to be sold, at what price should each be set? (Be careful with units when you do your calculations!)

The appropriate price = $

Answer 1

P =-.15q^2 + 59

Pq = Revenue = -.15q^3 +59q

R' = (Pq)'= -.45q + 59 = 0

q^2 = 59/.45 = 131 1/9

q = sqr(131.111...) = about 11.45 thousand = 11,450

P =-.15(59/.45) +59 = 39 1/3

Revenue Maximizing Price = $39.33

but if they only want to sell 9 thousand, then

P =-.15q^2 +59

P =-.15(9)^2 +59

= -.15(81) +59

= $46.84 = Price to sell 9,000, at a loss in Revenue, but maybe not in Profits, depending on costs