The profit for the Coffee Exchange company is given by P(x)=-15x 2 +180x-405 thousand dollars, where x is the number of tons of coffee beams produced…

The profit for the Coffee Exchange company is given by P(x)=-15×2+180x-405 thousand dollars, where x is the number of tons of coffee beams produced and sold,

a) what restriction does the physical nature of the model put on the domain of the function?

b) state the domain in interval notation:_______

c) will the vertex of the graph represent a minimum value or a maximum value?

d) How many tons of coffee beans should the Coffee Exchange produce and sell in order to maximize profit?