Linear Programming
Example
Define the Variables
x: Number of cars built
y: Number of trucks built
Does it matter?
Vertices of the Boundary
Constraints and Feasible Region
Cars: x-axis
Trucks: y-axis
Constraints
Wheels: 4 x  6 y  36
Seats:2 x  y  14
NonNegative
x0
y0
 0, 0   7, 0  Gas Tanks: x  3 y  15
 6, 2   3, 4 
Graph the System:
 0,5
Test Point
(0,0)
Feasible Region
0  36 True
0  14 True
0  15 True
Critical Points and Conclusion
Write an equation to represent Otto’s total profit (P) if he
makes $1 on each car and $2 on each truck
P = x + 2y
Test every critical point in the profit equation to see which
combination of cars and trucks will maximize the profit
3, 4
3  2  4  11
 6, 2 
6  2  2  10
 0,5
0  2  5  10
 0, 0 
 7, 0 
0  2  0  0
7  2  0  7
CONCLUSION:
Otto should build 3 cars and 4 trucks for $11.