NECO 2023 · Paper 1 · Q49

Linear programming & operations research

The corner points of the feasible region of a problem are $A(0, 3)$ , $B(2, 3)$ , $C(4, 3)$ , $D(3, 4)$ and $E(0, 0)$ . If $P = 35x + 40y$ , what is the maximum value of $P$ ?

Worked solution (try it first)

The greatest value of $P$ is at a corner of the feasible region, so work out $P = 35x + 40y$ at each.
$A$ : 120.
$B$ : $70 + 120 = 190$ .
$C$ : $140 + 120 = 260$ .
$D$ : $105 + 160 = 265$ .
$E$ : 0.
The maximum is 265, at $D(3, 4)$ , option E.

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