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:
\(3x+5y\ge 15\)
\(x+6y\ge9\)
\(x \ge 0\; ; y\ge 0\)