Question 1. A firm, DLS Apps, Inc. decides to enter the market for apps made for teenagers and children. Their Production Supervisor analyzed each of the operations and concluded that if the company produces apps for children, each app would require 8 hours in the theme creation department, 12 hours in the graphics and imaging department, 4 hours in the educational content department, 6 hours in the coding department, and 5 hours in the testing and launching department. On the other hand, each app for teenagers would require 4 hours in the theme creation department, 15 hours in the graphics and imaging department, 15 hours in the educational content department, 10 hours in the coding department, and 2 hours in the testing and launching department. After studying the departmental workload projections, the Production Supervisor estimates that 100 hours for theme creation, 250 hours for graphics and imaging, 200 hours for the educational content creation, 150 hours of coding and 50 hours for the testing and launching are available for the production of the new apps during the next four months.
The accounting department analyzed the costs based on the production data and overheads and arrived at prices for the apps that will result in a profit contribution of $10,000 per children’s app and $15,000 per teenager app produced. The CEO asserts that to be successful in the long run, at least 5 children’s apps must be launched in the next four months. The management is trying to identify how many apps of each type should they launch in the next four months and have hired you to help them figure out what the optimal solution would be and what the expected profits would be.
1. Write out the Linear Program (equations)
2. Provide the optimal solution, either graphically or by using Excel Solver. What is the total expected profit? How many apps of each type would you recommend that they make?
3. Identify which constraints are binding.
4. Which department has the highest slack? How much?
5. If the company was able to obtain 5 more hours in the coding department, would the profit change? Explain why or why not.
Ch.8: LP:Sensitivity Analysis
Question 2. Chrissy is a health and fitness coach. She wants to create a nutritional supplement, which meets the required daily dose of key nutrients at the lowest cost. Her goal is to sell this blend to her own clients to ensure that their nutritional needs are met in the most efficient manner possible. She decides to combine three different protein powders in order to create her own blend. The price of Type A Protein Powder is $25 per pound and it contains 42 gms of protein, 12 gms of carbohydrates and 4 gms of fat per serving. The price of Type B Protein Powder is $10 per pound and it contains 20 gms of protein, 20 gms of carbohydrates and 2 gms of fat per serving. The price of Type C Protein Powder is $8 per pound and it contains 10 gms of protein, 5 gms of carbohydrates and 10 gms of fat per serving. Each pound of any protein powder is equivalent to 12 servings. Chrissy runs a cost minimization linear program and identifies the blend would result in the lowest cost of $15.94 per pound of her own mix in order to meet the minimum requirements of 60 gms of protein, 45 gms of carbohydrates, and 20 gms of fat per serving. Her sensitivity report is given here. Based on the report, answer the following questions:
1. Write out the Linear Program (equations) that Chrissy might have used.
2. What is the optimal solution that Chrissy obtained? Total Minimum Cost?
3. Specify the objective function ranges. What do they mean? (in words)
4. Identify each of the Right-Hand Side ranges. What do they mean? (in words)
5. Interpret the shadow prices of each constraint (in words)

Ch.10: Network Problems: Linear Programming
Question 3. GreenClean Bamboo Products, Inc. produces sustainable paper products such as bath rolls and paper towels using bamboo instead of wood. The CEO of GreenClean, Annika Janeway, wants to ensure that a steady, adequate flow of bamboo to the four paper-processing plants is maintained to capitalize on the growing demand for sustainable products in the market. The bamboo arrives from four major locations and the distance from each location to the processing plants is shown in the figure below. Annika’s goal is to ensure that the transportation costs are minimized to the extent possible in order to maintain profitability in the company. The average haul cost is $2 per mile for both loaded and empty trucks because the company uses biofuel to minimize their carbon footprint. The intake manager has estimated the number of truckloads of bamboo that can be obtained from each location every week. The processing managers at each plant have estimated the truckloads of bamboo their plants require every week. These estimates are also provided in the figure below. Answer the questions following the figure:

1. Draw the Network Diagram showing costs of transportation and write out the Linear Program to minimize the costs of transportation
2. Use Solver to obtain the optimal solution and clearly demonstrate how many truckloads should be sent from each land area and to which plants. Also, clearly specify what the total cost of the transportation is per week. Draw the Final Network Diagram as well.
Ch.14: Inventory Models
Question 4. TP Inc. is a small company specializes in supplying toilet paper to small businesses, offices, universities, restaurants, and other similar establishments in the city of San Antonio. TP Inc. purchases their stock from brand-name toilet paper manufacturers and has significant limitations on its ability to carry an exceptionally large inventory. Despite the small business style, the company is immensely popular and gets enough clients that the demand is not deterministic in nature, but instead, follows a probabilistic pattern. The Manager of TP Inc. would like a recommendation on how many packages of toilet paper to order and when to order in an effort to minimize the inventory costs. You are provided the following pertinent information regarding the company and costs. Answer questions (a.), (b.) and (c.) given below
• Ordering Cost is $100.00 per order
• Cost of each package of toilet paper is $9.00 per box for TP Inc.
• The company uses a 25% annual holding cost rate for its inventory
• The lead time for a new order of toilet paper is 8 days
• Sales data indicate that the demand during 8-day lead time follows a normal probability distribution with a weekly mean of 750 boxes and a standard deviation per week of 80 boxes.
• The number of working days per year is 330
• Acceptable probability of a stock-out is 1% or 0.01.
1. What is the current EOQ?
2. What is the current Reorder point?
3. The manager is also considering increasing the risk of stockouts from 1% to 10%. Do you think that would help him reduce costs? Explain why.
Ch.13: PERT/CPM
Question 5. During the Corona-Quarantine, Emily decides to teach her kids how to bake cookies. She wants to take the opportunity to practice her own PERT/CPM project management skills as well. So, she lists out the activities that are required to bake two batches of cookies including the predecessors (if any) for each activity and the optimistic, most probable, and pessimistic time (in minutes) it takes to complete each activity; especially since she knows that everything can take longer when working with children. Some of the timings are fixed (e.g. baking or cooling times) so you will see that she has the same values for the optimistic, most probable, and pessimistic times.
1. Create the network diagram and create the activity schedule.
2. Identify which activities have slack time.
3. What is the probability that Emily is able to successfully finish and put away both batches of cookies within 54 minutes?

Ch.15: Waiting Line Models
Question 6. During the Coronavirus pandemic, Bobby’s restaurant is only open for drive-through and wants to provide quick service to their customers to minimize the risk of exposure. They currently have assigned one lane to serve the drive-through crowd. Bobby recognizes that having a lengthy line is likely to deter other customers from arriving at the restaurant. Now, Bobby needs to figure out if he needs to open a second drive-through lane or not. He spends a couple of days to observe the patterns of arrival for customers and notes how long it takes for service to be provided to each customer from the time they enter the drive-through lane until they leave. He finds that the average time between the arrivals of customers is about 1 minute with a “give and take” of about 30 seconds (0.5 minutes). He also notices that the average service time is about 45 seconds (0.75 minutes) per customer with a “give and take” of about 45 seconds (0.75 minutes). He estimates the hourly cost of having a queue would be about $15 per customer lost and his cost of opening a new lane would be about $20 per hour. Should Bobby open up another lane? Does he need another lane, or can his restaurant sustain as is? What would you recommend he should do? HINT: the “give and take” refers to “standard deviation”.