Optimization constraints for types of oil

Question

I'm looking at a lecture online which shows the following problem

They have two types of oil and they want to produce standard and premium gasoline. However i'm confused how they've arrived at the constraints $2x_1+6x_2 \geq h_1$ and $3x_1+3x_2 \geq h_2$ and this was not explained in the lecture just skipped over. Surely if $h_1$ is the demand for standard gasoline with $x_1$ units of national oil the most we could make is $x_1/2$ units of standard gasoline and likewise $x_2/6$ with imported oil but they have $2x_1$ and $6x_2$. Also why are they being added together? Could someone explain the derivation of the constraints?

Answer 1

It seems these two constraints are still the problem definition. As mentioned, for standard gasoline you need 2 and 6 units of x1 and x2 (oils) respectively, and since the demand for standard gasoline is h1, the production must be equal or greater than that.

Answer 2

Too long for comment.

Your confusion is valid, the constraint $2x_1+6x_2\ge h_1$ does not make sense. Say, $x_1=2$ units of national oil, $x_2=6$ units of imported oil and the demand for standard gas is $h_1=40$. The constraint is satisfied, however, with the given input ($x_1=2,x_2=6$) it can be produced only $1$ unit of standard gas.

I assume the decision variables should be units of output (standard and premium gas), not input.