SOLUTION: You are about tot take a test that contains questions of type A worth 10 points and questions of type B worth 25 points. you must do at least 3 questions of type A but time restric

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You are about tot take a test that contains questions of type A worth 10 points and questions of type B worth 25 points. you must do at least 3 questions of type A but time restric      Log On


   

Question 850855: You are about tot take a test that contains questions of type A worth 10 points and questions of type B worth 25 points. you must do at least 3 questions of type A but time restricts doing more than 12. you must do at least 4 questions of type B but time restricts doing more than 15 in total you can do no more than 20 questions.
How many of each type of question must you do to maximize your score? what is the maximum score?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
A linear optimization problem.

x = how many type A questions to do
y = how many type B questions to do

CONDITIONS
3%3C=x%3C=12;
4%3C=y%3C=15;
x%2By%3C=20.

score function, v.
v=10x%2B25y

Make a graph showing all of the conditions. Pick each vertex of the figure formed and check it in the formula of v. Choose the combination of x and y which give the largest value for v.