Question

Maximize the objective function P = 3x + 5y for the given constraints.I’m not sure if 19 is correct

Answer 1

Given,

The function is,

P = 3x + 5y

The constraint are,

$\begin{gathered} x\ge0 \\ y\ge0 \\ x+y\leq5 \\ 3x+6y\leq21 \end{gathered}$

The graph of the inequalities is,

The maximum value is,

At (0, 3.5)

$P=3x+5y=3\times0+5\times3.5=17.5$

At (3, 2)

$P=3x+5y=3\times3+5\times2=19$

At (5, 0)

$P=3x+5y=3\times5+5\times0=15$

Hence,the maximum value is 19.