Determine the number of each grill (super, deluxe) that should be made this week in order to maximize profit?

You are studying "linear programming".

You have a number of variables:
Let "x" = the number of super grills to make,
Let "y" = the number of …

You want to maximize the (linear) profit function:
profit = f(x,y) = …

Subject to several constraints:
Amount of iron is at most 6850 kilograms. Write an inequality in x and y.
Amount of labour is at most 95 hours. (How many minutes?) Another inequality.
At most 150 super grills. Yet another inequality, but a very simple one!

Finally some common sense inequalities:
x is greater than or equal 0.
y is greater than or equal 0.

These constraints define a polygon. The maximum will be at a vertex. Since this is only 2 dimensional, it is easy to draw the graphs (on a computer if you are lazy like me) and find the vertices. The gradient of the profit function (if you know what that is) can help determine which vertex will be the maximum. (The gradient tells you in which direction the profit function is increasing. At a maximum point, the gradient must be pointing out of the constraint polygon, making an angle of at least 90 degrees with the edge to both sides. So at a vertex, of which there are only a finite number to check.)

One last complication. You probably want only whole number answers, but some of the vertices are not integral points. In this case, you have to do a little extra "trimming", cutting off non-integral corners from the nearest integral points on each edge.