A company manufactures backpacks. The total cost to make each backpack, including materials and labor, is $23. In addition, the company has expenses of $12,000 per month for items such as rent, insurance, and utilities; these expenses do not depend on the number of backpacks made. Thus, a linear model for expenses would be E = 23B + 12000 where E is the company's total monthly expenses (in dollars) B is the number of backpacks produced in a month. We also have information about the number of backpacks sold each month, depending on the price of the backpack. Price ($) 30 35 40 45 50 Number of Backpacks Sold 10,000 7,200 6,200 5,300 3,500 Based on this information, we can compute the revenue each month. Revenue=Price*Number of Backpacks 1. (15 points) In MATLAB, write a script file named Backpacks 1.m that (a) Defines a vector B with range from 0 to 14,000, using increments of 100. (b) Defines a vector E that is calculated using the linear model given above for each value in the vector B. (c) Defines a vector P that contains all of the prices in the table above. (d) Defines a BSold that contains all the data for the number of backpacks sold in the table above. (e) Defines a vector R that is revenue generated at each price based on the number of backpacks sold (data given in chart above); use the formula above. (f) Plot (on one graph) B and E using a solid line and BSold and R using * for the data points. Add a title, of your choice, to the graph. Label the horizontal axis Number of Backbacks and the vertical axis Expenses/Revenue. Add a legend with labels for "Expenses" and "Revenue" and make sure to position the legend such that it doesn't cover any of the information on the graph. Insert a copy of your plot into the word procesing file you are creating to turn in. 2. (5 points) Analyze the graph you created in #1. Is the company making or losing money? How do you deduce this? 3. (10 points) Now, add the following to the script file Backpacks1.m that you started in #1: (a) Define a new vector Expenses that is calculated, using the linear model given above, for each value in the vector B Sold. (b) Define a new variable Profit, representing the profit in a given month. Profit=Revenue-Expenses (c) Create a new figure. (d) Plot BSold versus Profit. Use a *- in your graph; thus, each data value is represented by a * and the data points are connected with straight lines. Add an appropriate title and axes labels to your graph. Insert a copy of your plot into the word procesing file you are creating to turn in. Turn in a copy of your MATLAB file. 4. (10 points) Profit (a) If your minimum production is 3,500 backpacks a month and your maximum pro- duction is 10,000 backpacks a month, use the information from #3 to determine what is the optimal number of backpacks to produce to maximize profit. Explain how you arrived at this conclusion. (b) What additional data or information that would be helpful to determining a (pos- sibly) more accurate answer to #4a? Explain why this would be helpful. A company manufactures backpacks. The total cost to make each backpack, including materials and labor, is $23. In addition, the company has expenses of $12,000 per month for items such as rent, insurance, and utilities; these expenses do not depend on the number of backpacks made. Thus, a linear model for expenses would be E = 23B + 12000 where E is the company's total monthly expenses (in dollars) B is the number of backpacks produced in a month. We also have information about the number of backpacks sold each month, depending on the price of the backpack. Price ($) 30 35 40 45 50 Number of Backpacks Sold 10,000 7,200 6,200 5,300 3,500 Based on this information, we can compute the revenue each month. Revenue=Price*Number of Backpacks 1. (15 points) In MATLAB, write a script file named Backpacks 1.m that (a) Defines a vector B with range from 0 to 14,000, using increments of 100. (b) Defines a vector E that is calculated using the linear model given above for each value in the vector B. (c) Defines a vector P that contains all of the prices in the table above. (d) Defines a BSold that contains all the data for the number of backpacks sold in the table above. (e) Defines a vector R that is revenue generated at each price based on the number of backpacks sold (data given in chart above); use the formula above. (f) Plot (on one graph) B and E using a solid line and BSold and R using * for the data points. Add a title, of your choice, to the graph. Label the horizontal axis Number of Backbacks and the vertical axis Expenses/Revenue. Add a legend with labels for "Expenses" and "Revenue" and make sure to position the legend such that it doesn't cover any of the information on the graph. Insert a copy of your plot into the word procesing file you are creating to turn in. 2. (5 points) Analyze the graph you created in #1. Is the company making or losing money? How do you deduce this? 3. (10 points) Now, add the following to the script file Backpacks1.m that you started in #1: (a) Define a new vector Expenses that is calculated, using the linear model given above, for each value in the vector B Sold. (b) Define a new variable Profit, representing the profit in a given month. Profit=Revenue-Expenses (c) Create a new figure. (d) Plot BSold versus Profit. Use a *- in your graph; thus, each data value is represented by a * and the data points are connected with straight lines. Add an appropriate title and axes labels to your graph. Insert a copy of your plot into the word procesing file you are creating to turn in. Turn in a copy of your MATLAB file. 4. (10 points) Profit (a) If your minimum production is 3,500 backpacks a month and your maximum pro- duction is 10,000 backpacks a month, use the information from #3 to determine what is the optimal number of backpacks to produce to maximize profit. Explain how you arrived at this conclusion. (b) What additional data or information that would be helpful to determining a (pos- sibly) more accurate answer to #4a? Explain why this would be helpful