Question 3 - A-Level Maths

Given that $k$ is a constant, complete the Simplex tableau below for the following linear programming problem. Maximise $$P = k x + 6 y + 5 z$$ subject to $$\begin{gathered} 2 x + y + 4 z \leqslant 11
x + 3 y + 6 z \leqslant 18
x \geqslant 0 , y \geqslant 0 , z \geqslant 0 \end{gathered}$$
Use the Simplex method to perform one iteration of your tableau for part (a), choosing a value in the $\boldsymbol { y }$-column as pivot.
1. In the case when $k = 1$, explain why the maximum value of $P$ has now been reached and write down this maximum value of $P$.
2. In the case when $k = 3$, perform one further iteration and interpret your new tableau. \section*{Answer space for question 3}
$\boldsymbol { P }$ $\boldsymbol { x }$ $\boldsymbol { y }$ $\boldsymbol { Z }$ $s$ $\boldsymbol { t }$ value
1 $- k$ -6 -5 0 0 0
0
0
$\boldsymbol { P }$ $\boldsymbol { x }$ $\boldsymbol { y }$ $\boldsymbol { Z }$ $\boldsymbol { s }$ $\boldsymbol { t }$ value
\section*{Answer space for question 3}
1. $\_\_\_\_$