Suppose that a MAX problem contained the following constraint: $5$x $+8$y $40.$ Then which of the following statements is true?

For the point $(1,4),$ the slack for this constraint would have a value of $3.$

For the point $(8,5),$ the slack for this constraint would have a value of $40.$

For the point $(4,2),$ the slack for this constraint would be zero.

For the point $(4,2\mathrm{.}5),$ the slack for this constraint would be a positive value. $2.$Consider a linear programming model with the objective of profit maximization. Let Xi $=$ the number of units to produce of product i$.$ The objective function coefficients should typically be:

Group of answer choices

profit per unit.

selling price per unit.

variable cost per unit.

revenue per unit. $3.$There are $50$ hours of production time available in a given department. The department produces three products and their production times are as follows: $($X$8$ minutes$),($Y$4$ minutes$),($Z$7$ minutes$).$ The correct resource availability constraint is:

Group of answer choices

$\mathrm{.}13$X $+\mathrm{.}06$Y $+\mathrm{.}11$Z $50$

$8$X $+4$Y $+7$Z $3000$

$8$X $+4$Y $+7$Z $50$

$8$X $+4$Y $+7$Z $30004.$Any change in the values for the RHS $($Right Hand Side$)$ of a binding constraint of an LP problem will:

Group of answer choices

change the slope of the that constraint

change the slope of the objective function

not change the slope of the constraint but move it parallel to the original

not change the feasibility region $5.$Which of the following statements is FALSE regarding employee staffing applications?

Group of answer choices

It is possible to have multiple optimal solutions in employee staffing applications.

The goal of employee staffing problems is typically to determine how many employees need to start their work at the different starting times permitted.

Employee staffing problems can be formulated as assignment problems.

The employee staffing problem is a extension of the product mix problem.

Based on the requirements and constraints, it is possible for an employee staffing problem to become infeasible. $6.$Consider the following constraint: X$140.$ This implies that at most $40$ units of product X$1$can be produced.

Group of answer choices

True

False $7.$ The "Sinking Fund" problem can be classified as a multi$-$period linear programming application.

Group of answer choices

True

False $8.$Consider the following linear programming model:

Max$$ X$21+$ X$2+3$X$3$

Subject to:

$$ X$1+$ X$23$

$$ X$1+$ X$21$

$$ X$1,$ X$20$

This problem violates which of the following assumptions?

Group of answer choices

certainty

integrality

proportionality

linearity

divisibility $9.$ A linear programming model generates an optimal solution with fractional values.$$ This solution satisfies which basic linear programming assumption?

Group of answer choices

certainty

divisibility

proportionality

linearity

non$-$negativity