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in Linear Programming by (50.2k points)
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A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of Type A screws requires 2 minutes on the threading machine and 3 minutes on the slotting machine. A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine. In a week, each machine is available for 60 hours.

On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws.

Formulate this problem as a LPP given that the objective is to maximise profit.

Solve the linear programming problem and determine the maximum profit to the manufacturer.

1 Answer

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Best answer

Let’s consider that the company manufactures x boxes of type A screws and y boxes of type B screws.

From the given information the below table is constructed:

From the data in the above table, the objective function for maximum profit Z = 100x + 170y

Subject to the constraints

2x + 8y ≤ 3600 ⇒ x + 4y ≤ 1800 … (i)

3x + 2y ≤ 3600 … (ii)

x ≥ 0, y ≥ 0 (non-negative constraints)

Therefore, the required LPP is

Maximize: Z = 100x + 170y

Subject to constraints,

x + 4y ≤ 1800, 3x + 2y ≤ 3600, x ≥ 0, y ≥ 0.

The objective function for maximum profit Z = 100x + 170y

Subject to constraints,

x + 4y ≤ 1800 …. (i)

3x + 2y ≤ 3600 … (ii)

x ≥ 0, y ≥ 0

Now, let’s construct a constrain table for the above

Table for (i)

Next, solving equations (i) and (ii), we get

x = 1080 and y = 180

It’s seen that OABC is the feasible region whose corner points are O(0, 0), A(1200, 0), B(1080, 180) and C(0, 450).

On evaluating the value of Z, we have

Form the table it’s seen that the maximum value of Z is 138600.

Therefore, the maximum profit of the function Z is 138600 at (1080, 180).

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