HW 2 Solutions

The linear programming problem below is infeasible. Max Z = 5x1 + 3x2 s.t. 4x1 + 3x2 ≤ 8 x1 ≤ 4 x2 ≤ 6 x1, x2 ≥ 0

FALSE

The linear programming problem below is unbounded. Min Z = 5x1 + 3x2 s.t. 4x1 + 3x2 ≥ 8 x1 ≥ 4 x2 ≥ 6 x1, x2 ≥ 0

FALSE

the correct way to implement a sensitivity analysis for the second coefficient of the objective function is to vary not only the second coefficient but also the first one (at the same time).

FALSE

If one of the coefficients of the objective function is changed to a value outside of its respective sensitivity range (greater than the upper limit or lower than the lower limit), the optimal solution will be different than the one originally obtained before the change is implemented.

TRUE

Sensitivity analysis is a way to deal with uncertainty in linear programming models.

TRUE

Consider the following linear programming problem: Min Z = 7x1 + 5x2 Subject to: 4x1 + 3x2 ≥ 200 2x1 +x2 ≥70 x1, x2 ≥ 0 What is the upper limit of the first coefficient of the objective function (c1)?

a) 10

The following linear programming problem has _________________ Max Z = $5x1 + $10x2 Subject to: 8x1 + 5x2 ≤ 80 2x1 + 1x2 ≤ 100 x1, x2 ≥ 0

a) only one optimal solution

Consider the following linear programming problem: Min Z = 7x1 + 5x2 Subject to: 4x1 + 3x2 ≥ 200 2x1 +x2 ≥70 x1, x2 ≥ 0 What is the lower limit of the second coefficient of the objective function (c2)?

3.5

Consider the following linear programming problem: Min Z = 7x1 + 5x2 Subject to: 4x1 + 3x2 ≥ 200 2x1 +x2 ≥70 x1, x2 ≥ 0 What is the upper limit of the second coefficient of the objective function (c2)?

5.25

Sensitivity ranges can be computed only for the coefficients of the objective function

FALSE

an optimal solution for a company that is able to produce two different products (x1 and x2) is x1 = 0 and x2 = 6. The best strategy for this company is to produce only x1.

FALSE

The properties of a linear programming problem are:

Proportionality, additivity, divisibility, and certainty

The following linear programming problem has _________________ Max Z = $200x1 + $100x2 Subject to: 8x1 + 5x2 ≤ 80 2x1 + 1x2 ≤ 100 x1, x2 ≥ 0

multiple optimal solutions

The following linear programming problem has _________________ Max Z = $30x1 + $15x2 Subject to: 8x1 + 5x2 ≥ 80 2x1 + 1x2 ≥ 100 x1, x2 ≥ 0 Please choose the option that would best fit the empty space above:

no solution, since it is unbounded

The following linear programming problem has _________________ Max Z = $40x1 + $10x2 Subject to: 8x1 + 5x2 ≤ 80 2x1 + 1x2 ≥ 100 x1, x2 ≥ 0

no solution, since it is unfeasible

The sensitivity range for an objective function coefficient is the range of values over which the current __________________ will remain optimal.

optimal solution

The Pinewood Furniture Company produces chairs and tables from two resources: labor and wood. The company has 120 hours of labor and 100 board-ft. of wood available each day. Demand for table is limited to 8 per day. Each chair requires 3 hours of labor and 4 board-ft. of wood, whereas a table requires 20 hours of labor and 9 board-ft. of wood. The profit derived from each chair is $100 and from each table is $500. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. The correct linear programming model formulation of this problem is:

100x1 + 500x2 3x1 + 20x2 ≤ 120 4x1 + 9x2 ≤ 100 x2 ≤ 8 x1, x2 ≥ 0

Consider the following linear programming problem: Min Z = 7x1 + 5x2 Subject to: 4x1 + 3x2 ≥ 200 2x1 +x2 ≥70 x1, x2 ≥ 0 What is the lower limit of the first coefficient of the objective function (c1)?

d) 6.67