Linear Programming?

Question

My book explains linear programming in the most confusing way that I don't understand and my teacher did not go over this at all! I'm so lost I need help:/

I have a problem that says "You are going to take a test than contains questions of type A worth 7 points and questions of type B worth 12 points. The total number of questions must be at least 8. You know that type A questions take 10 minutes and type B questions take 8 minutes and the maximum time for the test is 80 minutes, how many of each type of question must you do in order to maximize your score? What is the maximum score?"

I think I can figure those two questions out by using the 12 point questions and figuring it out but I have questions that go along with this saying determine the objective function and determine the system of constraint inequalities.

I know the objective function is C=Ax+By+K but how do I relate this equation back to my original problem? Please help!!!

Answer 1

Kari,

        The objective function (score) is S=7a+12b

The constraint equations are:

a+b>=8

10a+8b<=80

a>0

b>0

 

With a simple system like this if you plot the constraint equations a vs b they define a triangular region where the objective function is valid. The max S occurs at one of the vertexes of the triangle http://www.wolframalpha.com/input/?i=plot%28a%2Bb%3E8%2C10a%2B8b%3C80%2Ca%3E0%2Cb%3E0%29 you can see a plot here. 

a=0, b=10 gives S=120 which is the maximum score subject to the constraints.

 

Hope this helps

 

Jim

Answer 2

Number of problems:

A+B>=8

Score:

7A+12B = S

Time:

10A+8B<= 80