Question

a small firmmanufactures gold rings and chains . the totla number of rings and chain manufactured per day is atmost 24. it takes 1 hours to make a ring and 30 mins to make chains .the maximun hours available per day is 16.if the profit on per ring is 300 rs and taht on a chain is 190 rs , find the number of rings and chains taht should be manufactured per day , so as to earn the maximun profit

Answer 1

Let’s start by defining the variables:

Let x be the number of rings manufactured per day.

Let y be the number of chains manufactured per day.

The total number of rings and chains manufactured per day is at most 24. Therefore, we have:

x + y ≤ 24

It takes 1 hour to make a ring and 30 minutes to make a chain. Therefore, we have:

1x + 0.5y ≤ 16

The profit on each ring is Rs. 300 and that on each chain is Rs. 190. Therefore, the total profit can be calculated as:

Total Profit = 300x + 190y

We want to maximize the total profit. This can be done by solving the above equations using linear programming.

The solution to this problem is x = 12 and y = 12. Therefore, the firm should manufacture 12 rings and 12 chains per day to earn the maximum profit