The corner points of the feasible region determined by the system of linear constraints are as…
Mathematics20254 marksNumerical
The corner points of the feasible region determined by the system of linear constraints are as shown below:
Answer the following questions.
(a)[1.3333333333333333]
Let $Z = 3x - 4y$ be the objective function. Find the maximum and minimum value of $Z$ and also the corresponding points at which the maximum and minimum value occurs.
(b)[1.3333333333333333]
Let $Z = px + qy$ where $p, q > 0$ be the objective function. Find the condition on $p$ and $q$ so that the maximum value of $Z$ occurs at $B(4,10)$ and $C(6,8)$.
(c)[1.3333333333333333]
State the number of optimal solutions in this case.
Answer
Answer (a)
Official answer key
$Z$ is minimum at $A(0, 8)$ and $Z_{\min} = -32$,
$Z$ is maximum at $E(4, 0)$ and $Z_{\max} = 12$.
Final answer: $Z_{\min} = -32$ at $A(0,8)$; $Z_{\max} = 12$ at $E(4,0)$
Answer (b)
Official answer key
At $B(4, 10)$, $Z = 4p + 10q$
At $C(6, 8)$, $Z = 6p + 8q$
As $Z$ is maximum for both cases, $4p + 10q = 6p + 8q \Rightarrow p = q$ is the required condition.
Check your working with the LPP solver (graphical method): linear programming by the graphical method: the feasible region drawn, corner points and the optimum.
