Operations Mangement OT1

Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Considering that the values for x and y that will maximize revenue are respectively x = 0 and y = 8, what is the amount of slack/surplus associated with the first constraint - in the optimal point?

0

Slack variables are only associated with maximization problems.

False

Consider the following linear programming problem: Max Z = $200x1 + $100x2 Subject to: 8x1 + 5x2 ≤ 80 2x1 + x2 ≤ 100 x1, x2 ≥ 0 What is maximum Z and the value of x1 and x2 at the optimal solution?

Z = 2000; x1 = 10; and x2 = 0;

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:

Max Z = 100x1 + 500x2 Subject to: 3x1 + 20x2 ≤ 120 4x1 + 9x2 ≤ 100 x2 ≤ 8 x1, x2 ≥ 0

Administrators at a university are planning to offer a summer seminar. It costs $4000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $45 per student for the administrators to provide the course materials. If we know that 100 people will attend, what price should be charged per person to break even?

$85

Consider the following linear programming problem: Max Z = 4x1 + 2x2 Subject to: x1 4 x2 2 x1, x2 ≥ 0 The Z obtained from the best combination of x2 and x1 is:

20

_______________refers to the ability of an organization to sell products in a market. Please choose the option that best fits the empty space above.

Business Competitiveness

The break-even point is the volume that the profit is positive (greater than zero).

False

If by processing the same amount of inputs used in the past a company is now capable to produce a(n) ________ amount of outputs, it means that an improvement of productivity was achieved.

Greater

Considering the following LP problem: Min Z = 23x1 +38x2 subject to: 3x1 + 6x2 ≤ 90 9x1 - 8x2 ≥ 30 2x1 + 10x2 ≤ 50 -5x1 + 8x2 ≤ 100 x1,x2 ≥ 0 Which one of the following option is correct:

none of the above Answers: The problem is infeasible The problem is unbounded There are more than one optimal solution (0 , 5) is the optimal solution

When building a mini-boat, a boat builder uses 2 pounds of wood and 3 ounces of glue. If he/she has 3 pounds of wood and 6 ounces of glue, how many mini-boat(s) will he/she be able to build?

none of the above: zero two four six

Australian road freight company Linfox uses aerodynamic trucks and trailers to reduce fuel consumption. This is a case of generating higher

productivity

Which of the following combinations of constraints has no feasible region?

x1 + x2 15 and x1 - x2 10 x1 + x2 5 and x1 10 x1 + x2 100 and x1 + x2 50 x1 + x2 10 and x1 5 All of the above have a feasible region.