A company makes two products , namely X and Y. Each product must be processed in 3 stages; welding , assembly and painting.
Each unit X takes 2 hours in welding, assembling 3 hours and 1 hour in painting.
Each unit Y takes 3 hours in welding, 2 hours assembling and 1 hours in painting.
The Total hours worked by employees for one month is 1500 hours for welding, 1500 hours for assembling and 550 hours for painting . The contribution to profits is IDR 1,000,000 for product X and IDR 1.200.000 for product Y
Determine :
a) The objective function (Z) to maximize the linear program.
b ) The constraint equations for an employee working hours welding in this linear program
c ) Find a solution to this linear programming problem (the value of X and Y ) if the company's profit is maximized . How much of IDR the maximum profit ?
Please help me..
a) To maximize profits, we need to define the objective function (Z). In this case, the objective function is the total profit. The total profit can be calculated by multiplying the number of product X by its contribution to profit (IDR 1,000,000) and the number of product Y by its contribution to profit (IDR 1,200,000) and then summing them up.
Let's define:
- X as the number of product X
- Y as the number of product Y
The objective function (Z) can be written as:
Z = (1,000,000 * X) + (1,200,000 * Y)
b) Now, let's define the constraint equations for the employee working hours in welding. We are given that the total hours worked by employees for one month in welding is 1500 hours. Each unit of X takes 2 hours in welding, and each unit of Y takes 3 hours in welding. So, the constraint equation for welding can be written as:
(2 * X) + (3 * Y) = 1500
c) To find a solution to this linear programming problem and determine the maximum profit, we need to optimize the objective function Z while satisfying all the constraints.
One way to solve this linear programming problem is by using the method of graphical analysis. However, in this case, the constraints are not easily graphable due to the presence of multiple variables and constraints. Therefore, we can use the Simplex Method or any other suitable optimization algorithm to solve the linear programming problem and find the optimal values of X and Y.
The values of X and Y can then be used in the objective function to calculate the maximum profit (Z).
Please note that without additional information such as constraints on the number of units produced or inventory constraints, we cannot determine the exact values of X and Y, or the maximum profit. Additional constraints would be required to find a specific solution.