The LP relationships that follow were formulated by Richard Martin at the Long Beach Chemical Company.

Maximize $8x_1+\frac{1}{2}{x}_1{x}_2+5x_3$

Subject $to$: $7x_1{x}_2+2x_{3}70$

$,3\mathrm{.}9x_1-4x_{2}15\mathrm{.}6$

$,4x_1+3x_2+3x_{3}21$

$,12x_2-\frac{1}{3}{x}_3=17$

$,-9x_1-x_2+4x_3=5$

$,7x_1+2x_2+3\sqrt[\phantom{2}]{x_3}80$

For an LP$,$ the objective function developed by Richard is

Constraint $C1$ is $a(n)$ LP constraint.

Constraint $C2$ is $a(n)$ LP constraint.

Constraint $C3$ is $a(n)$ LP constraint.

Constraint C$4$ is a$($n$)$ LP constraint.

Constraint $C5$ is a$($n$)$ LP constraint.

Constraint C$6$ is a$($n$)$ LP constraint.