I just need some pointers or a lead. I'm getting to my wits end with what I thought would be a simple problem. I just need help defining what the objective function is or what the variables are because it seems to me all the variations I try are useless. Thank you.
It looks to me like you have two variables- x, the number of days factory 1 is run, and y, the number of days factory 2 is run. You will then produce x+ 2y units of A grade steel and 3x+ 2y units of grade B steel. The cost will be \(\displaystyle 5000x+ $6000y\). The problem wants you to minimize the cost so that is the objective function. Minimize that subject to the constraints that \(\displaystyle x+ 2y\ge 80\) and \(\displaystyle 3x+ 2y\ge 140\).