The question goes as follows-
A company makes a specialty solvent at two levels of purity, which it sells in gallon containers. Product $A$ is of higher purity than product $B$, and profits are \$$0.40$/gal on $A$ and \$$0.30$/gal on $B$. Product $A$ requires twice the processing time of B. If the company produced only $B$, it could make $100$ gal/day. However, process throughput limitations permit the production of only $800$ gal/day of both $A$ and $B$ combined. Contract sales require that at least $200$ gal/day of B be produced.
Assuming all of the products can be sold, what volumes of $A$ and $B$ should be produced? Solve using the tableau form of the simplex method. Confirm your solution using graphical means.
I have tried to solve it in the following manner-
Let, $x_1,x_2$ be the volume (in gallon) of $A, B$ to be produced per day
Then we have to Maximize $Z=0.4x_1+0.3x_2$
Now, since in together only $800$ gal/day can be produced, we have $x_1+x_2\le800$
Again, since we have to make at least $200$ gal of $B$, we have $x_2\ge200$
From here, I can't proceed. I didn't understand the facts that $A$ requires twice the processing time of B and if the company produced only $B$, it could make $100$ gal/day.
What do these statements want to say? Where I will use it?
Can anybody solve this? Thanks for the assistance in advance.
If only $B$ is produced, we would get the maximum number of products of type $B$, then $x_2 \le 100$. Now since $A$ takes twice as long as $B$ to get produced, the maximum products of type $A$ which can be produced will be $50$, or $x_1 \le 50$.