solve mathematics

IE - 151

Midterm Exam

(Due date 3/11/2016 at 2:00pm)

Instructions: Solve the following problems individually. Once you’re done answering all questions, please copy and paste your solutions to this document. Also, make sure that you submit the Excel file that you used to solve the problems.

Part I. Boxplots

Problem 1. Download the data file “MidtermI.txt” and create a boxplot using Excel. Copy and paste the boxplot below (10 points);

Problem 2. Download the data file “MidtermI.txt” and create a boxplot using Minitab. Copy and paste the boxplot below (10 points);

Part II. Goal Seek

You must use goal seek to solve these problem. Take screenshots of the goal seek window showing your cell selections.

Problem 1. My wife Alice has a business that sells tea at a price of $2.49. Her cost of materials is $0.50 per cup of tea. In addition, she pays $130/day to rent the business space. Lastly, she has 3 employees that get paid $70/day. How many cups of tea does she have to sell in order to reach a profit of $500/day? (Hint: Profit = Revenue – Expenses) (10 points)

Problem 2. Mrs. and Mr. Jain, are starting their own street food business. They would like to figure out the number of Bhaji plates that they need to sell in order to have a profit of 1200 rupees per day. They sell each plate for 20.00 rupees. Their cost of materials is 8.00 rupees. They do not have to pay rent, but they pay 5.6% of the revenue in taxes. Determine how many plates of Bhaji they need to sell in order to reach their profit target of 1200 rupees per day. (Hint: Profit = Revenue – Expenses) (10 points)

Part III. Excel Solver (20 points)

Problem 1. I have a transportation company that delivers products from different factories to different destinations. I would like to find the cheapest way to deliver all of my product supply in order to satisfy all demand. The transportation cost will vary from source to destination. The transportation costs from all sources to all destinations are listed below.

In addition, I know that source 1 is able to supply 75 units, source 2 can supply 125 units, and source 3 can supply 100 units. Furthermore, I have a demand of 80, 65, 70, and 85 units at destination 1, destination 2, destination 3, and destination 4 respectively. I have created an initial Excel spreadsheet in order to solve this problem but I still need to do the following. (Download “MidtermIII.xlsx” from canvas)

a. Calculate the “Total Shipped” column for all sources. (Hint: Sum of quantity shipped from Source 1 to Destination 1, 2, 3 and 4 is =SUM(D12:G12))

b. Calculate the “Total Received” in all destinations. (Hint: Sum of quantity shipped from Source 1, 2, and 3 to destination 1 is =SUM(D12:D14))

c. Minimize the Total Cost (I18)

a. Variable Cells are cells D12:G14

b. Constraint 1: TotalShipped1 = Supply1

c. Constraint 2: TotalShipped2 = Supply2

d. Constraint 3: TotalShipped3 = Supply3

e. Constraint 5: TotalReceived1 = Demand1

f. Constraint 6: TotalReceived2 = Demand2

g. Constraint 7: TotalReceived3 = Demand3

h. Constraint 8: TotalReceived4 = Demand4

i. Select Solving Method: Simplex LP

Part IV. Distributions

Solve the following problems using Minitab. Take screenshots of your results and paste onto this document.

Problem 1. Calculate the CDF for x = 2, 4, 6, 8, 10. (10 points)

a. Normal distribution with mean of 15, and standard deviation of 10.

Problem 2. Download the data set “midtermIV.txt”

a. Determine the distribution of the data by using the Goodness of Fit Test. (10 points)

b. Determine the parameters of the distribution by using the probability plot method. (10 points)

Problem 3. Generate 50 random points based on a Normal distribution with a mean of 20 and a standard deviation of 10. (10 points)

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