brazil-enem 2016 Q148

brazil-enem · Other · enem__day2 Stationary points and optimisation Geometric or applied optimisation problem

Having a large piece of land, an entertainment company intends to build a rectangular space for shows and events, as shown in the figure.
The area for the public will be fenced with two types of materials:

on the sides parallel to the stage, a type A screen will be used, more resistant, whose value per linear meter is $\mathrm{R}\$ 20.00$;
on the other two sides, a type B screen will be used, common, whose linear meter costs $\mathrm{R}\$ 5.00$.

The company has $\mathrm{R}\$ 5000.00$ to buy all the screens, but wants to do it in such a way that it obtains the largest possible area for the public.
The quantity of each type of screen that the company should buy is
(A) $50.0 \mathrm{~m}$ of type A screen and $800.0 \mathrm{~m}$ of type B screen.
(B) $62.5 \mathrm{~m}$ of type A screen and $250.0 \mathrm{~m}$ of type B screen.
(C) $100.0 \mathrm{~m}$ of type A screen and $600.0 \mathrm{~m}$ of type B screen.
(D) $125.0 \mathrm{~m}$ of type A screen and $500.0 \mathrm{~m}$ of type B screen.
(E) $200.0 \mathrm{~m}$ of type A screen and $200.0 \mathrm{~m}$ of type B screen.

Having a large piece of land, an entertainment company intends to build a rectangular space for shows and events, as shown in the figure.

The area for the public will be fenced with two types of materials:
\begin{itemize}
  \item on the sides parallel to the stage, a type A screen will be used, more resistant, whose value per linear meter is $\mathrm{R}\$ 20.00$;
  \item on the other two sides, a type B screen will be used, common, whose linear meter costs $\mathrm{R}\$ 5.00$.
\end{itemize}
The company has $\mathrm{R}\$ 5000.00$ to buy all the screens, but wants to do it in such a way that it obtains the largest possible area for the public.

The quantity of each type of screen that the company should buy is

(A) $50.0 \mathrm{~m}$ of type A screen and $800.0 \mathrm{~m}$ of type B screen.

(B) $62.5 \mathrm{~m}$ of type A screen and $250.0 \mathrm{~m}$ of type B screen.

(C) $100.0 \mathrm{~m}$ of type A screen and $600.0 \mathrm{~m}$ of type B screen.

(D) $125.0 \mathrm{~m}$ of type A screen and $500.0 \mathrm{~m}$ of type B screen.

(E) $200.0 \mathrm{~m}$ of type A screen and $200.0 \mathrm{~m}$ of type B screen.

Paper Questions

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