linear inequality question

Question

This is a application of linear programming question and I am unsure of how to properly set up the equations. 

 

A factory that makes statuettes is trying to maximize its income. Their two primary products are the Venus and David statuettes. Each Venus requires 45 minutes of machine time to rough cut the shape and 16 minutes of craftsman time to finish the details. The David requires 60 minutes on the machines and 8 minutes with the craftsman's hand. The factory is limited each day to 540 minutes of machine time and 128 minutes of craftsman time. Both use 50 pounds of stone, and the factory has 500 pounds of stone available per day. If each Venus brings in a profit of fifty dollars, and each David brings in ninety-four dollars, how many statuettes of each type should the factory make each day

Answer 1

Let the x-axis represent the number of Davids and the y-axis represent the number of Venuses  

 

The machine time constraint gives the inequality 60X + 45Y ≤ 540  

 

The craftsman time constraint gives 8X + 16Y ≤ 128  

 

The stone weight constraint gives 50X + 50Y ≤ 500  

 

And of course they cannot make less than 0 statuettes so we have X ≥ 0 and Y ≥ 0  

 

The income equation is I = 94X + 50Y  

 

That's the set up.  Let me know if you need more help solving or want to check an answer