A company can use two types of machine A and B in a munifucturing plant number of operators required and the running cost per day are given as

cost per day avialable operators floor area (m) profit per machine
machine A 6 2 2 20
machine B 3 4 2 30
maximum available 360 280 160
A wite down the inequality constriants and the profit function
B group the inequality from the group detet the number of machines A and B which should be used to maximize profits

1. The inequality constraints are as follows:

- Number of operators: 2A + 4B ≤ 280
- Floor area: 2A + 2B ≤ 160
- Cost per day: 6A + 3B ≤ 360
- Non-negativity constraint: A, B ≥ 0

The profit function is:

Profit = 20A + 30B

To maximize the profit, we need to solve the system of inequalities by graphing or using optimization techniques. In this case, we can use linear programming to find the optimal values of A and B.

We can rewrite the inequalities in the standard form for linear programming:

- 2A + 4B + s1 = 280
- 2A + 2B + s2 = 160
- 6A + 3B + s3 = 360
- A, B, s1, s2, s3 ≥ 0

Using a linear programming solver, we can find that the maximum profit is obtained when we use 40 machines of type A and 40 machines of type B.

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