Point $(2,4)$ is feasible for the constraint $3x_1+5x_{2}30.$

T $6.$ At the optimal solution, constraints with positive slack are non$-$binding.

$F$

$7.$ Uncontrollable inputs are the decision variables for a model.

Section $2-$Multiple Choice $(3$ points each, one bonus question is included$)$

Surplus

a$.$ is the difference between the left and right sides of a constraint.

$b.$ is the amount by which the left side of $a$ constraint is smaller than the right side.

c$.$ is the amount by which the left side of $a$ constraint is larger than the right side.

d$.$ exists for each variable in a linear programming problem.

e$.$ None of the above.

For the products $A,B,C,$ and $D,$ which of the following could be a linear programming objective function?

a$.P=1A+3BC+3D$

b$.P=5A+2\frac{A}{B}+3$ABC$+4$ABCD

c$.P=1A+2^B+3C$

d$.P=7\mathrm{.}7A+2\mathrm{.}7B-3\mathrm{.}25C+4\mathrm{.}4D$