hw 1 ops management

The sensitivity range of c1 (profit per x1, bowls) in the Beaver Creek Pottery example was 25 ≤ c1 ≤ 66.67. For whatever reason, it became less profitable to produce bowls, so c1 decreased from US$40 to US$32. Considering that c1 is now US$32, what is the correct statement regarding the current sensitivity range of c1?

The lower limit didn't change

By changing the layout of its manufacturing plant, a company was able to produce more products per day, by using the same amount of resources. This is a case of generating higher __________.

productivity

Consider the following linear programming problem: Max Z = $30x1 + $10x2 s.t. 30x1 + 70x2 ≤ 210 20x1 + 10x2 ≤ 100 x1, x2 ≥ 0 What is maximum Z and the value of x1 and x2 at the optimal solution?

None of the above

Administrators at a university are planning to offer a summer seminar. It costs $6000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $75 per student for the administrators to provide the course materials. If we know that 60 people will attend, what price should be charged per person to break even?

175

When building a mini-boat, a boat builder uses 1 pound of wood and 2 ounces of glue. If he/she has 9 pounds of wood and 6 ounces of glue, how many mini-boat(s) will he/she be able to build?

3

The graph below represents a LP problem in which the objective function is "Minimization" and parallel to the constraint 1. Which one of the following answers would best indicate how the best Z can be obtained in the problem below?

All the points from the segment of line "AB"

If by processing a greater amount of input used in the past a company is now producing a(n) ________ amount of output, it means that an increase of productivity was not achieved. Please choose the option that best fits the empty space above.

exactly the same

Consider the following linear programming problem: Max Z = $12x1 + $5x2 Subject to: 8x1 + 5x2 ≤ 30 4x1 + 3x2 ≤ 12 x1, x2 ≥ 0 Considering that the values for x1 and x2 that will maximize revenue are respectively x1 = 3 and x2 = 0, what is the amount of slack/surplus associated with the first constraint ("8x1 + 5x2 ≤ 30") in the optimal point?

6

The graph below represents a LP problem in which the objective function is "Maximization" and parallel to the constraint 1. Which one of the following answers would best indicate how the best Z can be obtained in the problem below?

None of the above

Considering the following LP problem: Max Z = 5x1 + 12x2 s.t. x1 + x2 >= 25 3x1 + x2 >= 45 5x1 + 7x2 >= 20 7x1 + 13x2 <= 83 x1, x2 >= 0 Which one of the following options is correct?

The problem is infeasible

The break-even point is the volume of production that allows the company to have a greater revenue comparing to its total cost.

false

Consider the following linear programming problem: Max Z = 4x1 + 2x2 s.t. x1 ≤ 4 x2 ≤ 8 x1, x2 ≥ 0 The Z obtained from the best combination of x1 and x2 is:

32

For the given objective function which of the following combinations of constraints would produce multiple optimal solutions? Max Z = 10x1 +6x2

5x1 + 3x2 <= 15 and x1 + x2 <= 10

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

All of the above have a feasible region.

The Pinewood Furniture Company produces chairs and tables from two resources: labor and wood. The company has 145 hours of labor and 100 board-ft. of wood available each day. Demand for chair is limited to 8 per day. Each chair requires 3 hours of labor and 4 board-ft. of wood, whereas a table requires 22 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 + 22x2 ≤ 145 4x1 + 9x2 ≤ 100 x1 ≤ 8 x1, x2 ≥ 0