1. Linear Programming
Mr. Carpenter
Alg. 2

2. Linear Programming Scenario
A manufacturer can make a profit of $6 on a bicycle and a profit of $4 on a tricycle. Department A requires 3 hours to manufacture a bicycle and 4 hours to manufacture a tricycle. Department B takes 5 hours to assemble a bicycle and 2 hours to assemble a tricycle. How many bicycles and tricycles should be produced to maximize the profit if the total time available in Department A is 450 hours and in Department B is 400 hours?
Optimizing Equation:
6x + 4y = I
Constraints:
3x + 4y ≤ 450
5x + 2y ≤ 400
Define the variables:
X = # of bicycles produced
Y = # of tricycles produced

3. Graph Constraints Constraints: 3x + 4y ≤ 450 5x + 2y ≤ 400
Solved for y:
y ≤ -3/4 x
Y ≤ -5/2 x + 200

4. Find the vertices (0, 11) (8, 0) (5, 7.5)
Vertices are the extremes of the “area of feasibility”
(0, 11)
(8, 0)
(5, 7.5)

5. Finding the maximum
Optimizing Equation: 6x + 4y = I 3 vertices tested: (0, 11): 6(0) + 4(11) = 44 (8, 0): 6(8) + 4(0) = 48 (5, 7.5): 6(5) + 4(7.5) = 60
By producing 50 bicycles and 75 tricycles we make the maximum amount of income: $600.00