Heres the schedule for two items A and B. Given the construction time below:
Item A:
Machine 1- 2 hours
Machine 2- 3 hours
Packaging- 5 hours
Item B:
Machine 1- 1 hours
Machine 2- 1 hours
Packaging- 1 hours
The labour hours per week are as follows: machine 1, 80 hours; machine 2, 50 hours; packaging, 70 hours. If the profit on each item A and B are $7 and $2 respectively, how many of each item should be made weekly in order to maximize profit? What is the max profit?
To find the number of each item that should be made weekly in order to maximize profit, we need to consider the available labor hours and the time required for each task.
Let's first calculate the total time required to produce each item:
Item A:
Machine 1: 2 hours
Machine 2: 3 hours
Packaging: 5 hours
Total time for Item A: 2 + 3 + 5 = 10 hours
Item B:
Machine 1: 1 hour
Machine 2: 1 hour
Packaging: 1 hour
Total time for Item B: 1 + 1 + 1 = 3 hours
Now, we can determine the maximum number of each item that can be produced based on the available labor hours:
Machine 1: 80 hours
Machine 2: 50 hours
Packaging: 70 hours
For Item A:
The bottleneck resource is Machine 1, which has a maximum of 80 hours available. Since Item A requires 2 hours on Machine 1, the maximum number of Item A that can be produced is 80 / 2 = 40.
For Item B:
The bottleneck resource is also Machine 1, which has a maximum of 80 hours available. Since Item B requires 1 hour on Machine 1, the maximum number of Item B that can be produced is 80 / 1 = 80.
Next, we need to consider the profitability of each item. The profit per item is given as $7 for Item A and $2 for Item B.
To maximize profit, we need to consider the profit contribution of each item and produce more of the item with higher profit contribution.
Profit contribution for Item A = (Number of Item A * Profit per Item A) = (40 * $7) = $280
Profit contribution for Item B = (Number of Item B * Profit per Item B) = (80 * $2) = $160
Since the profit contribution for Item A is higher than that of Item B, we should produce more of Item A to maximize profit.
Therefore, the maximum number of each item that should be made weekly to maximize profit is:
Item A: 40
Item B: 0 (as producing more Item A will maximize profit)
And the maximum profit achievable is $280.