Q. 3

# Maximise z = x + 2y

Subject to the constraints

x + 2y ≥ 100

2x – y ≤ 0

2x + y ≤ 200

x, y ≥ 0

Solve the above LPP graphically. **[CBSE 2017]**

**[CBSE 2017]**

Answer :

x + 2y = 100 ...(1)

2x - y = 0 ...(2)

2x + y = 200 ...(3)

x = 0, y = 0 ...(4)

Draw the graph of lines (1), (2), (3) & (4) and then find the corner

points.

Corner points are A(100, 0), B(50, 100), C(20, 40)

Thus, Maximum is at point B and maximum value is 250.

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PREVIOUSA small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and a half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ₹ 100 and that on a bracelet is ₹ 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced. [CBSE 2017]NEXTSolve the following L.P.P. graphically :Minimize Subject to Constraints and [CBSE 2017]

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