Solution

The correct answer is y ≤ 7.5, 2x + 3y ≤ 8, 3x + 2y ≤ 10

Key Points

To formulate the constraints for the linear programming problem (LPP), we need to consider the availability of the three kinds of wool (red, green, and blue) and the requirements for each type of cloth.

The constraints are based on the following:

• One unit length of type A cloth needs 2 yards of red wool and 3 yards of green wool.
• One unit length of type B cloth needs 3 yards of red wool, 2 yards of green wool, and 2 yards of blue wool.
• The firm has a stock of 8 yards of red wool, 10 yards of green wool, and 15 yards of blue wool.

Here are the constraints broken down:

• Red wool constraint: \(2x + 3y \leq 8\)
• Green wool constraint: \(3x + 2y \leq 10\)
• Blue wool constraint: \(2y \leq 15\)  =>  y ≤ 7.5

Given these constraints, the correct formulation is: y ≤ 7.5, 2x + 3y ≤ 8, 3x + 2y ≤ 10