Question 1

Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even?

Accepted Answer

To break even, the total revenue from ticket sales must equal the total cost of hosting the seminar.
Let x be the number of students who register.
Total revenue = $150x
Total cost = $3000 + $25x
To break even,
$150x = $3000 + $25x
$125x = $3000
x = 24
Therefore, the university would need 24 students to register to break even.

Question 2

Linear mathematical programming techniques assume that all parameters in the models are

Accepted Answer

Linear mathematical programming techniques assume that all parameters in the model are known with certainty. This means that the values of the parameters are fixed and can be precisely determined, rather than being uncertain or subject to variation.

Question 3

It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario?

Accepted Answer

The correct constraint for the scenario is the total cost of cat and dog food combined must be less than or equal to $40. Since cat food costs $0.50 per can (C) and dog food costs $1 per can (D), the equation .5C + 1D ≤ 40 represents the maximum amount Lisa can spend on cat and dog food within her budget.

Question 4

A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is:

Accepted Answer

The correct constraint combines the pounds of flour used per batch of each product and the maximum flour available. Each batch of bread (x1) uses 4 pounds, cookies (x2) use 3 pounds, and muffins (x3) use 2 pounds, with a total limit of 24 pounds. Thus, the equation is 4x1 + 3x2 + 2x3 ≤ 24.

Question 5

Which one of the following techniques is not a mathematical programming technique?

Accepted Answer

The analytical hierarchy process (AHP) is a multicriteria decision-making technique used to rank and prioritize alternatives based on a set of criteria. While it involves mathematical calculation, it is not considered a mathematical programming technique, unlike the other options presented which are all types of mathematical programming.

Question 6

An objective function

Accepted Answer

The answer of An objective function
...

Question 7

Decision support systems and sensitivity analysis are useful management science tools for answering the question:

Accepted Answer

Decision support systems (DSS) are designed to help managers make informed decisions by analyzing data and presenting potential scenarios based on that data. Sensitivity analysis, which involves testing the effect of different variables on the outcome of a decision, is an important component of DSS. Together, these tools help managers answer the question "what if?" by exploring different scenarios and assessing the potential impact of different decisions.

Question 8

It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is an appropriate objective function for this scenario?

Accepted Answer

The objective function should minimize the cost of the food. Since dog food costs twice as much as cat food, the objective function should reflect that by multiplying the number of cans of dog food by 1 and the number of cans of cat food by 0.5. Therefore, the appropriate objective function is Min Z = 1D + 0.5C.

Question 9

Marriott used which of the following management science techniques to help improve profit by $120 million over two years?

Accepted Answer

Marriott used forecasting to predict demand, simulation to model different scenarios, and optimization to determine the best course of action in order to improve profits.

Question 10

Which of the following statements is false?

Accepted Answer

Decision models do not consider all factors from the real world. Instead, they selectively consider the relevant factors and ignore the irrelevant ones to simplify the problem and focus on the key variables.

Question 11

A difficult aspect of using spreadsheets to solve management science problems is

Accepted Answer

Setting up a spreadsheet with complex models and formulas can be a difficult aspect of using spreadsheets to solve management science problems. This requires a good understanding of both spreadsheet software and the management science models being used. Data entry can also be time-consuming, but it is generally straightforward. Obtaining the solution to standard management science problems and performing sensitivity analysis are typically easier once the spreadsheet model has been properly set up.

Question 12

EKA manufacturing company produces part #2206 for the aerospace industry. The unit production cost of part #2206 is $3. The fixed monthly cost of operating the production facility is $3000. Next month's demand for part #2206 is 200 units. How much should the company charge for each unit of part #2206 to break even?

Accepted Answer

The total cost of producing 200 units is $3000 (fixed cost) + 200 x $3 (unit production cost) = $3600. To break even, the company must charge $3600 / 200 = $18 per unit.

Question 13

A bed-and-breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $6000 per month and the revenue they receive from each booked room is $180. What is their variable cost per occupied room?

Accepted Answer

The answer of A bed-and-breakfast breaks even every month if...

Question 14

Decision analysis is a ________ technique.

Accepted Answer

Decision analysis involves analyzing and assessing various possible outcomes based on probabilistic or uncertain inputs. Thus, it is a probabilistic technique. The other options listed (linear mathematical programming, network analysis, and non-linear programming) are all different techniques used in operations research and decision-making, but they are not applicable to decision analysis specifically.

Question 15

Which one of the following management science methods is not a probabilistic technique?

Accepted Answer

Assignment models are deterministic, meaning they do not involve uncertainty or probability in their basic form. They are used to allocate resources to tasks in the most efficient way possible without considering randomness.

Question 16

Larry's Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $160. The objective function that minimizes these costs for Larry is:

Accepted Answer

The objective function that minimizes costs for Larry is "Min 5S + 3.5W" because it represents the goal of minimizing the total cost of purchasing salmon (S) and whitefish (W), with their respective costs per pound.

Question 17

A technique that assumes certainty in its solution is referred to as

Accepted Answer

A deterministic technique assumes certainty in its solution, meaning that the outcome will always be the same given the same inputs and conditions. Stochastic and probabilistic techniques involve randomness and uncertainty in their solutions, and parametric techniques involve the use of parameters to estimate values in a statistical model.

Question 18

A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even?

Accepted Answer

To break even, the total revenue from the seminar needs to cover the fixed cost of $3000 plus the variable cost of providing course materials to 20 people (20 x $25 = $500).
Total cost = $3000 + $500 = $3500
To break even, the price per person would be:
$3500 ÷ 20 = $175
Therefore, the price per person should be $175 in order to break even.

Question 19

It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue is $45 per unit. What is the break-even point?

Accepted Answer

The break-even point is calculated by dividing the fixed costs by the difference between the unit selling price and the variable cost per unit. Here, it's $50,000 / ($45 - $25) = 2500 units.

Question 20

Classification of management science techniques does not recognize

Accepted Answer

The classification of management science techniques usually includes linear mathematical programming, probabilistic techniques, and network techniques. Computer programming is not usually considered a separate technique, but rather a tool used in conjunction with these other techniques.

Quiz 1: Management Science