Exercise 2 | Wiskunde op Tilburg University

Consider the revenue function

$R(x)=2x$ and the cost function

$C(x)=\sqrt{8x+32}$ . Determine all break-even points.

Antwoord 1 correct

Correct

Antwoord 2 optie

$x=-2$

Antwoord 2 correct

Fout

Antwoord 3 optie

$x=-2$ and

$x=4$

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=0$

Antwoord 4 correct

Fout

Antwoord 1 optie

$x=4$

Antwoord 1 feedback

Correct:

$\begin{align*} R(x) = C(x) & \Leftrightarrow 2x=\sqrt{8x+32}\ & \Rightarrow (2x)^2=8x+32\\ & \Leftrightarrow 4x^2=8x+32\\ & \Leftrightarrow 4x^2-8x-32=0\\ & \Leftrightarrow x^2-2x-8=0\\ & \Leftrightarrow (x-4)(x+2)=0\\ & \Leftrightarrow x=4 \mbox{ or } x=-2. \end{align*}$

Note that

$x=-2$ is no solution of

$R(x)=C(x)$ . Hence, the break-even point is

$x=4$ .

Go on.

Antwoord 2 feedback

Wrong: A production level cannot be negative.

See Break-even.

Antwoord 3 feedback

Wrong: A production level cannot be negative.

See Break-even.

Antwoord 4 feedback

Wrong: Profit should be zero, not the production level.

See Break-even.