Question

Need help in understanding and identifying correct Correct Objective Function of equations.
Please provide correct and wrong Objective function equation to understand the concept?

Answer 1

John Deere a company leader into Heavy machinery Production, they have two models to run their manufacturing unit, they are Pixef and FT2650, Resources are very limited, it includes 1000 Pounds of Raw Material and 40 Hours of production time each week, the marketing requirement for this job includes the production should not exceeds over 650 units each week, number of Pixef models can’t exceed number of FT 2650 Model by more than 400, again, Pixef require 2 pounds of Raw material and 4 Minutes of labor per unit, where as FT 2650 requires only 1 pound of Raw Material and 3 Minutes of labor per unit, again, profit per unit for pixef model is USD 80 and profit per unit for FT 2650 is USD 50,

Here, Correct Objective function is Maximize Z = 80*X1 + 50*X2, where as X1 = Number of units of Pixef model each week and X2 = Number of units of FT2650 model each week, any others objective functions could be treated wrong like Minimizing Z = 80*X1 + 50*X2, as we always need to maximize the profits, again, Maximize Z = 50*X1 + 80*X2(also wrong),

Subject to: or Constraints are:

2*X1 + 1*X2 =<1000,

4*X1 + 3*X2 =<40*60 = 2400,

X1 + X2 =< 650,

X1 – X2 =<400,

X1, X2>= 0 or Zero,(Non negativity)