need help please and thank you asap

Question

Steven owns a model airplane manufacturing business. Steven wants to maximize his revenue. He starts with the linear function x = -40p + 1600, where x is the predicted number of model airplanes he will sell at p dollars per airplane.

Based on this model, what is the maximum revenue in dollars that Steven would make selling his model airplanes?

Answer 1

  The demand is given in terms of the price as it should.

 BUT...

   We need the price in terms of X, the # of planes.

    So we have to find the inverse...

 

   x - 1600 = -40p

 

  (x-1600)/(-40) = p

 

 

Revenue function R(x) = quantity x price = x*P(x) = x(x-1600)/(-40)

 

The max occurs at the zeros of this parabola function.

The zeros are x=0 and x=1600

The average is 800.

 

So the max occurs for x=800 planes

(800 - 1600)/-40 = -800/-40 = 20

800 planes for $20