Optimization problem - Graphically How can we draw the cobb-douglas optimization problem with constraint and solve it graphically? 
We have the function $U(x,y)=x^{0.4}y^{0.3}$. 
Do we have to draw the constraint and some level curves of $U(x,y)$ ? 


Do we have to draw the constraint and some level curves of U(x,y) ?

That is right. I would recommend to use a function plotter since a single utility function only is hard enough to draw. You solve the utility function for y:
$$y=\left( \frac{\overline U}{x^{0.4}} \right)^{10/3}$$
For different levels of $\overline U$ the function plotter can draw different curves. 
For different values of $\overline U$ the array of curve looks like below

The different levels of $\overline U$ are 
$4.070905-3; \quad 4.070905-2.5; \quad4.070905-2;\quad 4.070905-1.5\quad \ldots \quad 4.070905+2$
From the graph you can read off that $(x^*,y^*)=(10,5)$
