contestada

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?

Respuesta :

[tex]x=375\:un\imaginaryI ts\:generate\:a\:maximum\:revenue\:of\:\$56,250.00[/tex]

1) Considering the Revenue function in the standard form:

[tex]R(x)=-0.4x^2+300x[/tex]

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

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

3) So, we can answer this way:

[tex]x=375\:units\:yield\:\$56,250[/tex]

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