1. Ahadu company produces two models of radios, modelA requires 20 min of work on assembly line 1 and 10 min of work on assembly line 1. Model B requires 10 min of work on assembly line I and 15 min of work on assembly line II. At most 22 hrs. of assembly time on line 1 and 25 hrs of assembly time on line II are available per week. It is anticipated that Ahadu company will realize profit of Birr 10 on model A and Birr 140 model. How many radios of each model should be produced per week in order to minimize Ahadu's profit
To determine the number of radios of each model that should be produced per week in order to minimize Ahadu's profit, we can use a linear programming approach.
Let's define the decision variables:
- Let X represent the number of radios of model A to be produced per week.
- Let Y represent the number of radios of model B to be produced per week.
Now, let's set up the objective function and constraints:
Objective function:
We want to minimize the profit, which can be expressed as: Profit = 10X + 140Y
Constraints:
1. Assembly Time on Line 1: 20X + 10Y <= 22 x 60 (converting hours to minutes)
This constraint ensures that the total assembly time on line 1 does not exceed the available 22 hours per week.
2. Assembly Time on Line 2: 10X + 15Y <= 25 x 60 (converting hours to minutes)
This constraint ensures that the total assembly time on line 2 does not exceed the available 25 hours per week.
Non-negativity constraints:
X >= 0 (The number of radios of model A cannot be negative)
Y >= 0 (The number of radios of model B cannot be negative)
Now, we can solve this linear programming problem using optimization techniques or software. The solution will give us the optimal values for X and Y, representing the number of radios of each model to be produced per week.
By solving the problem, we can determine the values of X and Y that will minimize Ahadu's profit.