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Solve the following linear programming problem.

Formulate the constraints which represent the above feasible region.

Mathematics20271 markShort answer
LPP Feasible Region
LPP Feasible Region

Answer

Answer

AI
The boundary lines of the feasible region are: 1. Line through $A(1,1)$ and $B(3,3)$: equation is $y = x \Rightarrow x - y \le 0$ (or $y - x \ge 0$). 2. Line through $B(3,3)$ and $C(1,7)$: slope is $\frac{7-3}{1-3} = -2$, equation is $y - 3 = -2(x - 3) \Rightarrow 2x + y \le 9$. 3. Vertical line through $A(1,1)$ and $C(1,7)$: $x \ge 1$. 4. Non-negativity constraints: $x \ge 0, y \ge 0$. Therefore, the constraints representing the feasible region are: $2x + y \le 9$, $x - y \le 0$, $x \ge 1$, $x \ge 0, y \ge 0$.
Linear Programming

From ISC 2027 Specimen Mathematics Paper 1, question 9(i).

Check your working with the LPP solver (graphical method): linear programming by the graphical method: the feasible region drawn, corner points and the optimum.