A company manufacture two products x snd y by means of two processes A and B .The maxinum capacity of processes A is 1750hours snd of process B 400.each unit of product X require 3 hours in A and 2hours in B while each unit of product Y requires 1 hour in A and 4 hours in B .How many units of products X and Y are produced if the maximum capacity svailable is utilized?
To find out the maximum number of units of products X and Y that can be produced, we need to calculate the number of units produced using each process separately and then determine the limiting factor that restricts the production.
Let's start by calculating the maximum capacity of each process:
Process A: Maximum capacity = 1750 hours
Process B: Maximum capacity = 400 hours
Next, let's determine how many units of product X can be produced using each process:
Process A:
Each unit of product X requires 3 hours.
Maximum number of units of X produced by process A = Maximum capacity of process A / Hours required per unit of X
= 1750 hours / 3 hours
= 583.33 units (rounded down to the nearest whole number)
Process B:
Each unit of product X requires 2 hours.
Maximum number of units of X produced by process B = Maximum capacity of process B / Hours required per unit of X
= 400 hours / 2 hours
= 200 units
Now let's determine how many units of product Y can be produced using each process:
Process A:
Each unit of product Y requires 1 hour.
Maximum number of units of Y produced by process A = Maximum capacity of process A / Hours required per unit of Y
= 1750 hours / 1 hour
= 1750 units
Process B:
Each unit of product Y requires 4 hours.
Maximum number of units of Y produced by process B = Maximum capacity of process B / Hours required per unit of Y
= 400 hours / 4 hours
= 100 units
Now we compare the maximum number of units produced by each process for both products:
- Product X: Process A (583 units) vs Process B (200 units)
- Product Y: Process A (1750 units) vs Process B (100 units)
Since Process A can produce more units for both products, it becomes the limiting factor. Therefore, the maximum number of units of products X and Y that can be produced utilizing the maximum capacity available is:
- Product X: 583 units
- Product Y: 1750 units