Sample Questions
Module 5 - Algorithms, Approximations and SimulationTest for Module 5
Problem 1 - Local routing II
The distances between the customer locations and the distribution centers in miles for a company that handles 3rd party logistics is as given below.
These are the number of boxes the customers need.
Vehicle routes
Ms. Ruby James is routing vehicles to deliver goods to seven customers. The customers are identified with an ID.
Consider that each of her trucks can carry, at most, 100 boxes per tour. Use the Savings algorithm to design the routes.
Tip: Remember that the Savings algorithm is a heuristic algorithm. This means that the solution provided by the Savings algorithm will not necessarily be the optimal solution to the problem.
Important: Write the sequence of customers with a dash between the ID numbers (do not use spaces and do not include “DC”). For example, if the route goes from DC to 5 to 2 to 6 to DC, write 5-2-6 or 6-2-5 (both are considered correct). In the above example, 2-5-6 or 2-6-5 would be considered wrong!
How many tours would Ruby need?
What are the savings (in distance traveled) compared to delivering directly from the DC to each customer?
Module 4 - Optimization
Problem 1 - Better Life Pharmacies
Part 1: Optimal order quantity
Nathan Wright is running a pharmacy in Nigeria (where Naira is the local currency). His recent experience in the MicroMasters course motivated him to rethink how to reorder pharmaceuticals to replenish inventory. He recalls from Module 4, Unit 1, Video 5, that he should consider the purchase cost, the order cost, and the holding cost. In the past, Joshua rigorously tracked these cost items. For Ibuprofen he knows that:
unit cost: = 176 Naira/pack
demand: = 770 packs/year
ordering cost: = 2100 Naira/order
holding cost: = 47 Naira/pack*year
How many packs of Ibuprofen should Joshua order to minimize the total cost?
Round your answer to the nearest integer.
Problem 2 - Softdrink production
Production plan for softdrinks
Marilyn James works in a juice firm and has to develop the production plan for the lemon and the orange juice concentrates. The fruits (lemon and orange) that she needs to make the juice are not the bottleneck but Marilyn is concerned about the other main ingredients that go into making the juice: a water-based solution, sugar, and a vitamin mix. Checking with the ERP system tells her that she has 9400 kg of the water solution, 3030 kg of sugar, and 1920 kg of vitamin mix. The recipe tells her to use 52 kg of water solution to make a metric ton of lemon drink and 78 kg of water solution to make a metric ton of orange drink. For the lemon drink she also needs 17 kg of sugar and 15 kg of vitamin mix. The orange drink needs 18 kg of sugar and 15 kg of vitamin mix.
From the sales department, Ina knows that the lemon soft drink sells at 54 SEK/ton and the orange drink sells at 74 SEK/ton. (SEK = Swedish krona).
How much lemon drink should Marilyn produce to maximize revenue?
How much orange drink should Marilyn produce to maximize revenue?
How much revenue can Marilyn generate with the optimal production plan?
Module 3
Test for Module 3
Problem 1: Fresh Now!
Part 2
To understand if the new concept has taken effect, Heather Rogers, the head of the analytics department, asks you to conduct a hypothesis test. Average daily profit per customer per store for the leafy vegetables in all other Fresh!Now! grocery stores is 14.
You formulate the following hypothesis test:
H0: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is not higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.
H1: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.
Calculate the test-statistic for the hypothesis test above.
Module 2 - ProbabilityTest for Module 2
Brinell & Rockwell
Brinell & Rockwell (B&R) is a high-end manufacturer of cutting and drilling bits for lathe machines, drill presses, and other metal-working equipment. They pride themselves in producing only bits of the very best quality, guaranteed to last longer than the bits from any of their competitors. Brinell & Rockwell has a hotline where customers can call to report when a B&R bit fails before it is expected. At that time, Brinell & Rockwell will ship a replacement bit to the customer free of charge, and the customer will return the failed bit for examination. Back at the Quality Control Department of Brinell & Rockwell, a team of scientists and engineers - including several with PhDs in Metallurgy - will examine the failed bits under the microscope, X-Ray machines, and other diagnostics equipment to determine exactly what went wrong.
Brinell & Rockwell's quality control team keeps the failed bits that they have collected from customers in large glass containers, using one glass container per bit model. They have gathered thousands of failed drilling and cutting bits of 73 different models, including 62 models of drilling bits. These 62 models of drilling bits can be grouped into four families:
In summary, they have collected failed bits of 73 different models, and they use one glass container for every bit model. Therefore, Brinell & Rockwell has in the lab a total of 73 different glass containers. Taking into account that drilling bits can be grouped into families, we know that 14 glass containers contain Diamond bits, 19 glass containers contain Tungsten bits, 20 glass containers contain Iridium bits, and 9 glass containers contain Adamantium bits.
Part 2
Theresa Sanders is the second worker to arrive to the lab. Following Brinell & Rockwell policy, she will pick two bits from randomly and independently selected containers. She is equally likely to select any of the containers. Even the container selected to pick up the first bit has the same chance of being chosen as any other container at the time she picks the second bit (meaning that Theresa could grab the same model of bit twice).
What is the probability that Theresa will pick up at least one Iridium bit?
Module 1: Problem 1: KNIT'ting Industries
You are a newly appointed consultant to KNIT'ting Industries and your task it to plan optimal production volumes of knitting wools. Knitting wools are some of the company's best selling products. KNIT'ting Industries imports high quality, colored knitting wools in large bundles from Asia, transports the wool to their plant in Europe, cuts and re-packages them into smaller units and sells them to the end consumer via their website.
Part 3: Revenue
2.0/2.0 points (graded)
Revenue from selling wool, SKU M30, can be modeled by multiplying demand and selling price. From the previous questions, we have an expression for demand as a function of selling price.
Use the answer from the previous question to find an expression for the daily revenue generated from selling wool as a function of the selling price.