The available quantity is $327$ gallons of red paint and $504$ gallons of diluting liquid. The below column shows how much red paint quantity (in gallons) and the diluting liquid (in gallons) is required to make a gallon of perfect paint for Product X and Product Y. Determine how many gallons of perfect paint can be produced for Product X and Product Y by optimum utilization of the available stock of red paint and diluting liquid.
Product X: | Product Y:
Red 0.255 | Red 0.405
Diluting 0.51 | Diluting 0.242
You will have a pair of equations:
$0.255X + 0.405Y \le 327$ (Based on the quantities of Red Paint)
and
$0.51X + 0.242Y \le 504$ (Based on the quantities of Diluting Liquid).
These are the two equations that you want to optimize.
If you solve these two simultaneously, and round down your final answer to whole numbers and you will have a solution.