1. ENGINEERING 2304 Computer Programming for Engineers ENGR 2304-51191 Spring 2015 Week 8

2. Class Outline Quiz Review Homework Excel Solver Function Matrices Matrix Addition/Subtraction Matrix Multiplication Practice Exercises

3. Week 8 Quiz 1.Download the week 8 quiz file from the learning web site. 2.Sort the data from states and territories of the lowest to the highest population. 3.On another tab, create a pivot table showing the quantity of states with one member in the US house, two members in the US house, three, etc. 4.Save the spreadsheet. Email it to the homework submittal address and with the standard homework submittal file format, except call it “Week 8 Quiz” instead of “Homework_.”

4. “I think life on Earth must be about more than just solving problems... It's got to be something inspiring, even if it is vicarious.” –Elon Musk

5. Quotes of the D “We must develop knowledge optimization initiatives to leverage our key learnings.–Scott Adams

6. Homework 6 Review

7. Excel Solver Add-in An optimization tool that allows to solve for a function or set of functions for a particular or minimum value. Can add constraints to a solution space limiting values to certain ranges. Target Cell: the cell that we are seeking to minimize, maximize, or set to a certain value or set to a certain Variable Cells: the independent variables that the solver will manipulate the target cell Constraints: conditions put in place on the target or variable cell.

8. Matrices Matrices are rectangular arrays of numerical values or expressions. “mxn” matrix refers to m rows, n columns. Matrices are useful for solving systems of equations and are at the core of many engineering software analysis packages. Examples: forces inside structural frames, currents inside circuits, etc.

9. Matrix Addition/Subtraction Matrix Addition/Subtraction is simply a matter of adding/subtracting corresponding rows and columns.

10. Matrix Multiplication In order to multiply one matrix by another, they must have matching dimensions. An axb can be multiplied by bxc into a axc matrix. Ex: [3x2]x[2x4]=[3x4] matrix [1x3]x[3x5]=[1x5] matrix [2x3]x[4x4] cannot be multiplied.

11. Example 1: Solver You operate a small electronics manufacturing company. You have $1 million to spend for the year and wish to maximize profit. Your company manufactures TVs, Stereos, and Cell Phones. TVs, Stereos, and Cell Phones cost $400, $50, and $200 to produce, respectively. TVs, Stereos, and Cell Phones cell for $1000, $100, and $300 each. You need to have at least 3 months of output in your warehouse at any given time to meet potential orders. TVs, Radios, and Cell Phones take up 5ft^2, 1 ft^2, and 0.5ft^2 of storage space, respectively. The size of your warehouse is 2000 ft^2. Must manufacture at least 150 of each. How many of each should you produce in order to maximize profit?

12. Example 2: Solver Optimize a simply-supported beam for a point load. Assume it’s a built-up member made from the same thickness plate, so web and flange thickness is the same. Check for both shear stress and bending stress.

13. Example 3: Matrices In Excel Work with entering, adding, subtracting, and multiplying matrices in Excel.