SOLUTION: Find the minimum and maximum values of the objective function subject to the given constraints. Objective Function: C=4x+3y Constraints: x is greater than or equal to 0

Algebra ->  Linear-equations -> SOLUTION: Find the minimum and maximum values of the objective function subject to the given constraints. Objective Function: C=4x+3y Constraints: x is greater than or equal to 0       Log On


   

Question 884657: Find the minimum and maximum values of the objective function subject to the given constraints.
Objective Function: C=4x+3y
Constraints: x is greater than or equal to 0
2x + 3y is greater than or equal to 6
3x - 2y is less than or equal to 9
x + 5y is less than or equal to 20
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the feasible region and vertices.
2x%2B3y%3E=6
graph%28300%2C300%2C-2%2C8%2C-2%2C8%2Cy%3E=%286-2x%29%2F3%29
.
.
.
3x-2y%3C=9
graph%28300%2C300%2C-2%2C8%2C-2%2C8%2Cy%3E=%283x-9%29%2F2%29
.
.
x%2B5y%3C=20
graph%28300%2C300%2C-2%2C8%2C-2%2C8%2Cy%3C=%2820-x%29%2F5%29
.
.

The vertices here were easy to find graphically but you could have solved for them algebraically also.
The extrema occur at the vertices.
.
.
.
(0,2):C=4%280%29%2B3%282%29=highlight%286%29
(0,4):C=4%280%29%2B3%284%29=12
(5,3):C=4%285%29%2B3%283%29=highlight%2829%29
(3,0):C=4%283%29%2B3%280%29=12