Solve the linear programming problem graphically: Maximise Z = 4x + y where x + y ≤ 50, 3x + y ≤ 90, x ≥ 0 and

Question 31 of 39

Q. Solve the linear programming problem graphically: Maximise Z = 4x + y where x + y \leq 50, 3x + y \leq 90, x \geq 0 and y \geq 0. (Graph sheet is not required).

West Bengal WbchseWest Bengal HS (WBCHSE) Board 2022Subjective· 5mImportance★★★★★

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In a linear programme, the optimum always occurs at a corner (vertex) of the feasible region — find all vertices and evaluate $Z$ at each.

Maximise $Z=4x+y$ subject to $x+y\le50$ , $3x+y\le90$ , $x\ge0$ , $y\ge0$ .

Step 1 — find the corner points of the feasible region.

Origin: $(0,0)$ .
On the $x$ -axis ( $y=0$ ): $x+0\le50\Rightarrow x\le50$ ; $3x\le90\Rightarrow x\le30$ . The binding (tighter) constraint gives vertex $(30,0)$ .
On the $y$ -axis ( $x=0$ ): $y\le50$ ; $y\le90$ . The binding constraint gives vertex $(0,50)$ . …

Q.Solve the linear programming problem graphically: Maximise Z = 4x + y where x + y ≤ 50, 3x + y ≤ 90, x ≥ 0 and y ≥ 0. (Graph sheet is not required).