The Greener Corporation produces electrical motorcycles and electric cars. The management wanted to produce at least 2 electrical cars and 8 electrical motorcycles but no more than 5 electric cars per month. The production department can produce a maximum of 20 electric cars and electrical motorcycles per month. The profit on each electric motorcycles is P20,000 while the profit on each electric car is P150,000. Find the required number of electric cars and electric motorcycles to get a maximum profit.
Linear programming problem.
number of cars --- x
number of bikes --- y
2 ≤ x ≤ 8
y ≤ 5
x+y ≤ 20
in the first quadrant, sketch these inequalities and shade in their common region.
( mine is a rectangle )
Which point is farthest from the origin ?
looks like we have points of interest at
(2,0) , (2,5), (8,5) and (8,0)
profit = 150000x + 20000y
at (2,0), profit = 300000
at (2,5), profit = 400000
at (8,5), profit = 1300000 -- that's the one
they should make 8 cars and 5 bikes
To find the required number of electric cars and electric motorcycles that will result in maximum profit, we can set up a linear programming problem.
Let's denote the number of electric cars as x and the number of electric motorcycles as y.
We are given the following constraints:
1. At least 2 electric cars: x ≥ 2
2. At least 8 electric motorcycles: y ≥ 8
3. No more than 5 electric cars: x ≤ 5
4. The production capacity is 20 for each type: x + y ≤ 20
We need to maximize the profit, which is calculated as follows:
Profit = (Profit per electric car * Number of electric cars) + (Profit per electric motorcycle * Number of electric motorcycles)
Profit = (150,000 * x) + (20,000 * y)
Let's solve this linear programming problem using graphical method:
Step 1: Graph the feasible region
- Plot the lines representing the constraints on a graph.
- Shade the region that satisfies all constraints.
Step 2: Identify the corner points of the feasible region
- The corner points of the feasible region are the vertices where the feasible region intersects.
Step 3: Calculate the profit at each corner point
- Plug the x and y coordinates of each corner point into the profit function to calculate the profit.
Step 4: Determine the corner point with the maximum profit
- Compare the profits obtained from step 3 and identify the corner point with the maximum profit. This will give us the required number of electric cars and electric motorcycles.
Applying these steps, we can determine the required number of electric cars and electric motorcycles to get the maximum profit.