Rutgers Operations Management

Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?

Constraint

Parameters are known, constant values that are usually coefficients of variables in equations.

True

Fixed costs depend on the number of items produced.

False

At the break-even point,

total revenue equals total cost.

In general, an increase in price increases the break-even point if all costs are held constant.

False

If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease.

False

A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. The break-even point is ____ units.

2,500

Variable cost does not include

staff and management salaries.

The purpose of break-even analysis is to determine the number of units of a product to sell that will

result in zero profit.

If fixed costs decrease, but variable cost and price remain the same, the break-even point

decreases.

A complete expression of the objective function might be written as Z=3X1 + 2X2 + 5*X3.

False

In the formulation of a ≥ constraint, to convert it into a standard form:

a surplus variable is subtracted.

Multiple optimal solutions can occur when the objective function is ______ a constraint line.

parallel to

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If its a minimization problem? What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB?

view quiz 2. E. B. -1.5

Most computer linear programming packages readily accept constraints entered in fractional forms, such as X1/X3.

False

The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

True

The sensitivity range for an objective function coefficient is the range of values over which the profit does not change.

False

For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________.

improvement, resource

When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed.

=SUMPRODUCT

The constraint x + y = z is written in standard form.

False

The three types of integer programming models are total, 0-1, and mixed.

True

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, rounding non-integer solution values up to the nearest integer value can result in an infeasible solution.

True

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, an optimal solution to an integer programming problem is ensured by rounding down non-integer solution values.

False

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise.

The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected.

Exactly 2 out of the 4

A rounded-down integer solution can result in a less-than-optimal solution to an integer programming problem.

True

Binary variables are

0 or 1 only.

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

x1+ x5≤ 1, x2 + x5 ≤ 1

Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.

Y1+ Y4 ≤1

Write the constraint the indicates they can purchase no more than three machines.

Y1+ Y2 + Y3+ Y4 ≤3

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is ________.

1

In a transportation problem, items are allocated from sources to destinations

at a minimum cost.

The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination.

source, demand

In a balanced transportation model where supply equals demand,

all constraints are equalities.

In an unbalanced transportation problem, if demand exceeds supply, the optimal solution will be infeasible.

False

In a transshipment problem, items may be transported

* from destination to destination.

* from one transshipment point to another.

* directly from sources to destinations.

Assignment linear programs always result in integer solutions.

True

The assignment problem constraint x41 + x42 + x43 + x44 ≤ 3 means

agent 4 can be assigned to no more than 3 tasks.

In an assignment problem all supply and demand values equal are:

1

In an assignment problem,

one task can be done by only one agent.

The difference between the assignment and the transportation problem is that

each supply and demand value is 1 in the assignment problem.

The slope of a curve at any point is equal to the derivative of the curve's function.

True

Maximum profit is achieved everywhere the first derivative of the profit function equals zero.

False

An optimal solution to a nonlinear programming problem will always occur at the boundary of the feasible solution space formed by the constraint.

False

In portfolio selection problems, the risk is measured by the variance of the return on the portfolio.

True

The slope of a curve at its highest point equals:

0

A profit function of Z = 3x^2 - 12x + 15 reaches minimum profit at x = ____ units of output.

2

Consider the curve 7x^2 - 14x + 28. What is the slope at x = 5?

56

If a firm's profit is Z = 12x - 6x^2 + 30, and their minimum production level of x is equal to 0.5, then the level of x that maximizes profit is:

1

A store has determined that the weekly sales of a product are related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x^2 - 10C^2 + 40Cx + 120x - 200. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales?

5

A custom molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4x2. An expression for the total contribution is:

60x1- 5x1^2+ 80x2 - 4x2^2