Question

The revenue function R in terms of the number of units sold, a, is given as R = 300x - 0.4x^2where R is the total revenue in dollars. Find the number of units sold a that produces a maximum revenue?Your answer is x =What is the maximum revenue?

Answer 1

`x=375\:un\imaginaryI ts\:generate\:a\:maximum\:revenue\:of\:\$56,250.00`

1) Considering the Revenue function in the standard form:

`R(x)=-0.4x^2+300x`

2) Since this is a quadratic function, we can write out the Vertex of this function:

`\begin{gathered} x=h=-(b)/(2a)=(-300)/(2(-0.4))=375 \\ k=f(375)=-0.4(375)^2+300(375)\Rightarrow k=56250 \end{gathered}`

3) So, we can answer this way:

`x=375\:units\:yield\:\$56,250`