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?
To solve this problem and determine the number of units Model A (A) and Model B (B) should produce to maximize the monthly profit, we can use linear programming.
Step 1: Define the decision variables:
Let A represent the number of Model A machines produced.
Let B represent the number of Model B machines produced.
Step 2: Formulate the objective function:
The objective is to maximize the monthly profit, which can be calculated using the following equation:
Profit = (25*A) + (40*B)
Step 3: Formulate the constraints:
Constraint 1: The total number of machines should not exceed 2500 per month:
A + B ≤ 2500
Constraint 2: The manufacturing cost should not exceed $600,000 per month:
(200*A) + (300*B) ≤ 600,000
Constraint 3: The number of machines produced cannot be negative:
A ≥ 0
B ≥ 0
Step 4: Set up the Linear Programming model:
Maximize: Profit = 25A + 40B
Subject to:
A + B ≤ 2500
200A + 300B ≤ 600,000
A ≥ 0
B ≥ 0
Step 5: Use a Linear Programming solver to find the optimal solution:
Using a Linear Programming solver, input the objective function, constraints, and variable bounds, and request the solver to maximize the objective function.
The solver will then compute the optimal solutions for A and B that maximize the monthly profit, while satisfying all the constraints.
It is important to note that since the number of units produced cannot be fractional, the optimal solution may result in whole numbers for A and B.
By following this linear programming approach, you can determine the number of Model A and Model B machines that should be produced to maximize the monthly profit.