SOLUTION: Kathy is doing a charity bake sale. She bakes two types of pies; sweet potato and milk pie. The pies sell for $12 and $15 respectively. Kathy has only 16 hours of time available an

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Kathy is doing a charity bake sale. She bakes two types of pies; sweet potato and milk pie. The pies sell for $12 and $15 respectively. Kathy has only 16 hours of time available an      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1033182: Kathy is doing a charity bake sale. She bakes two types of pies; sweet potato and milk pie. The pies sell for $12 and $15 respectively. Kathy has only 16 hours of time available and 10 cups of sugar. The baking time for sweet potato pies is 2 hrs. and milk pie is 3 hrs. Each sweet potato pies uses 3 cups of sugar and the milk pie uses 1 cup of sugar. What combination should she make to maximize profits?
I started off with:
R(X)= 12x + 15y
2x + 3y is less than or equal to 16
3x + y is less than or equal to 10
This is where I get stuck, can you please help?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the constraint equations to find the feasible region and the vertices.
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C2x%2B3y%3C=16%29
.
.
.
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C3x%2By%3C=10%29
..
.
.
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C%2816-2x%29%2F3%2C%2810-3x%29%29
.
.
.
There are four vertices to test.
(0,0)
(0,16%2F3)
(2,4)
(10%2F3,0)
I'll do one, you do the rest the same way.
(0,0): R=12%280%29%2B15%280%29=0 Obviously not the solution.
Check the other three vertices the same way.