Assignment Prompt & Instructions
1.
Which of the following functions is not linear?
Z
3X + 4Y + Z – 3
5X + 3Z
2X + 5YZ
Top of Form
**Question 2**
Which of the following is not one of the steps in formulating a linear program?
Graph the constraints to determine the feasible region.
Identify the objective and the constraints.
Use the decision variables to write mathematical expressions for the objective function and the constraints.
Define the decision variables.
**Question 3**
Media selection problems are typically approached with LP by either
maximizing audience exposure or minimizing advertising costs.
maximizing audience exposure or maximizing number of ads per time period.
minimizing the number of different media or minimizing advertising costs.
maximizing the number of different media or minimizing advertising costs.
**Question 4**
Which of the following is not an assumption of LP?
divisibility
certainty
proportionality
multiplicativity
**Question 5**
The term __________ refers to the expression that defines the quantity to be maximized or minimized in a linear programming model.
objective function
problem formulation
decision variable
association rule
**Question 6**
Which of the following is considered a decision variable in the media selection problem of maximizing audience exposure?
the amount spent on each ad type
the number of ads of each type
the overall advertising budget
what types of ads to offer
**Question 7**
The customer who arrives at a bank, enters a line, and decides to leave is
blithering.
cropping.
balking.
reneging.
**Question 8**
Lines at banks where customers wait for a teller window are usually representative of a
single-channel, single-phase system.
multichannel, single-phase system.
multichannel, multiphase system.
single-channel, multiphase system.
**Question 9**
Which of the following distributions is most often used to estimate the arrival pattern?
negative exponential
normal
Erlang
Poisson
**Question 10**
The customer who arrives at a bank, sees a long line, and leaves to return another time is
reneging.
balking.
cropping.
blithering.
**Question 11**
A single automatic car wash with one bay and a cycle time of 2.5 minutes is what type of model?
M/D/2
M/D/1
M/M/2
M/M/1
**Question 12**
A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times follow an exponential distribution. What type of queuing model is exhibited in this problem?
M/M/2
M/M/1
M/D/2
M/D/1
The following scenario should be used to answer questions 13-15:
Breeze Outdoors sells outdoor gear to adventure enthusiasts. They have a flexible advertising budget for the week, which they want to allocate across four media channels: sponsored podcasts, magazine ads, billboards, and influencer partnerships. The company has a priority to ensure that their podcast advertisements are featured at least twice per episode, but otherwise, they have given you full discretion to divide the budget as needed. The podcasts attract 30,000 dedicated listeners per episode and cost $3,000 per airing. The company also wants the ads to run at least twice per episode, which means you can allocate the rest of the budget as you wish. Magazine ads cost $2,000 each and can be placed up to four times a month. Each ad reaches 12,000 readers. For billboards, there are two options: one in high-traffic areas, and one in suburban neighborhoods. High-traffic billboards cost $2,500 each and reach 15,000 people per placement, whereas suburban billboards cost $1,200 and reach 7,000 people each. There are available slots for high-traffic billboards six times a week, and suburban billboards can be placed up to ten times a week. The influencer partnerships cost $1,500 each and reach 12,000 potential customers. The influencers usually post once a week, but their reach is impactful due to their large followings and high engagement rates.
**Question 13**
How many decision variables are in the Breeze Outdoors scenario? Define each one clearly.
Answer:
**Question 14**
Define the objective function if the goal is **to reach the most potential customers**.
**Question 15**
Define the objective function if the goal is to **identify the least expensive advertising campaign.**
**Question 16**
TireTech Inc. manufactures two types of tires: TrailBlazer SUV Tires and EcoRoll Hatchback Tires. The company wants to maximize its profit while considering resource limitations. Each tire produced travels through three departments: production, packaging, and shipping. Each TrailBlazer SUV tire requires 1.75 hours of production time, 1 hours of packaging time, and 0.75 hour of shipping time. Each EcoRoll Hatchback tire requires 1.25 hours of production time, 0.5 hour of packaging time, and 0.25 hour of shipping time. TireTech Inc. has available 425 hours of production time, 200 hours of packaging time, and 125 hours of shipping time. The profit margin per tire is $24 for the TrailBlazer and $16 for EcoRoll.
**Use the attached template to formulate and solve this as a linear programming problem.**
Answer the following questions clearly in the Excel file:
1. How many of each product should be produced?
2. What is the maximum profit that can be achieved?
3. Do any of the departments have leftover time? If so, how much?
**Question 17**
Bean There, Done That! is a popular coffee shop with a single drive-thru lane where customers order and pick up their drinks. Based on previous data, it is estimated that cars arrive at a rate of 15 per hour. Each car is served in 3.5 minutes on average. Assume that arrivals follow a Poisson distribution and service times follow an exponential distribution.
Choose the appropriate spreadsheet template for this problem, update it using the information provided above, and then clearly answer each of the following questions somewhere in the spreadsheet. When you are done, save the file and upload it back here.
1. What percent of the time is the employee at the drive-thru idle?
2. What is the average number of cars in line?
3. What is the average time (in minutes) each car spends waiting to reach the service window?
4. What percent of the time are more than 1 car in the drive-thru lane?
Round all answers to 1 decimal place.
**Question 18**
Grill & Go is a fast-casual restaurant focused on delivering hearty, grilled meals with a bold, smoky flavor profile. The menu is centered around high-quality, flame-grilled meats and fresh ingredients, aiming to provide a quick yet satisfying dining experience. Their staff includes both full and part-time workers to meet fluctuating demand during the day. The following table presents projected need for workers at different times of the day:
**Time**
**Minimum # of staff needed**
11-12
8
12-1
8
1-2
12
2-3
6
3-4
5
4-5
7
5-6
9
6-7
8
7-8
4
There has to be at least five, but no more than nine full-time staff; all other staff work part time shifts. Each full-time employee works from 11:00am until 8:00pm (with an hour meal break from 12-1pm) , while the part-time employees work for 5 consecutive hours at a cost of $19.00 per hour. The cost of the full-time worker is $175 per day.
**Use the attached template to formulate and solve this as a linear programming problem with the goal of minimizing the total daily cost.**
Answer the following questions clearly in the Excel file:
1. How many full-time employees should Grill & Go keep on their staff?
2. How many total part-time employees should Grill & Go use?
3. What is the minimum total daily cost?
4. At what time does the largest number of part time staff start their 5 hour shift?
**Question 19**
At the start of the theater season, the box office becomes busier the day before the opening show. Patrons arrive at the box office at the rate of six every 15 minutes. Each ticket agent can assist 8 patrons every 10 minutes, and there are traditionally two ticket agents working. The theater is considering replacing the agents with an automated kiosk that can assist a patron in 1.5 minutes. Assume each ticket agent earns $22 per hour, and the kiosk costs $40 per hour. The wait time cost is $4 per hour as patrons are willing to wait.
Update the attached template using the information provided above, and then clearly answer the question below. When you are done, save the file and upload it back here.
What is the total daily expected cost of each model if the box office is open for 10 hours each day?
**Question 20**
I certify that the answers I provided on the entirety of this test are my own and that I did not receive any unauthorized help to complete it.
Yes
No
– 2 years ago
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