Class 9th math 5.2 solution english PCTB

Note: This is the Solution of review exercise 5.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.

Exercise 5.2

Question # 01: Maximize \(\small{f(x,y)=2x+5y}\); subject to the constraints:

\(2y-x\le 8\)

\(x-y\le4\)

\(x \ge 0\; ; y\ge 0\)

Question # 02: Maximize \(\small{f(x,y)=x+3y}\); subject to the constraints:

\(2x+5y\le 30\)

\(5x+4y\le20\)

\(x \ge 0\; ; y\ge 0\)

Question # 03: Maximize \(\small{f(x,y)=2x+3y}\); subject to the constraints:

\(2x+y\le 4\)

\(4x-y\le4\)

\(x \ge 0\; ; y\ge 0\)

Question # 04: Maximize \(\small{z=2x+y}\); subject to the constraints:

\(x+y\ge 3\)

\(7x+5y\le35\)

\(x \ge 0\; ; y\ge 0\)

Question # 05: Maximize the function defined as; \(\small{f(x,y)=2x+3y}\); subject to the constraints:

\(2x+y\le 8\)

\(x+2y\le 14\)

\(x \ge 0\; ; y\ge 0\)

Question # 06: Find minimum and maximum values of \(\small{z=3x+y}\); subject to the constraints:

\(3x+5y\ge 15\)

\(x+6y\ge9\)

\(x \ge 0\; ; y\ge 0\)

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