PLEASE HELP!!!!!!!
machines A &B.
Model A machines each cost $200 to make at a profit of $25 each. Model B cost $3oo to make at a $40 profit. Total number of machines do not exceed 2500 a month. Company has no more $600,000 per month for manufacturing cost. Whats the number of units A and B should produce to maximize the monthly profit?
maximize 25a + 40b
a + b <= 2500
200a + 300b <= 600000
Make 2000 machine B for a profit of 80,000
Thanks Steve for the answer:
maximize 25a + 40b
a + b <= 2500
200a + 300b <= 600000
Make 2000 machine B for a profit of 80,000
To determine the number of units of Model A and Model B that should be produced to maximize the monthly profit, we need to set up a mathematical model based on the given information.
Let's assume:
- x = the number of units of Model A produced
- y = the number of units of Model B produced
According to the given information, the following can be derived:
1) The manufacturing cost equation:
The manufacturing cost of producing x units of Model A and y units of Model B should not exceed $600,000:
200x + 300y ≤ 600,000
2) The total number of machines equation:
The total number of units produced cannot exceed 2500 per month:
x + y ≤ 2500
3) The profit equation:
The profit made per unit of Model A is $25, and the profit made per unit of Model B is $40:
Profit = (25x) + (40y)
The objective is to maximize the profit function subject to the given constraints.
To do this, we can use a linear programming method called the graphical method. Here are the steps:
Step 1: Graph the feasible region.
- Plot the region satisfying the constraints from equations 1) and 2) on a Cartesian plane.
Step 2: Identify the corner points of the feasible region.
- The corner points of the feasible region are the vertices of the shaded region.
Step 3: Evaluate the profit function at each corner point.
- Calculate the profit at each corner point using the profit equation (Profit = (25x) + (40y)).
Step 4: Determine the corner point with the maximum profit.
- Identify the corner point that corresponds to the maximum profit value.
Step 5: Calculate the number of units of Model A and Model B at the corner point with maximum profit.
- Evaluate the value of x and y at the corner point with the maximum profit to determine the optimal solution.
Please keep in mind that due to the complexity of calculating and graphing this problem, it would be easier to use appropriate software or tools such as Excel or dedicated linear programming software to solve this problem accurately.