Spring 2023 Name: You must show appropriate work to support your answers to receive credit. Show work on separate paper and only put final answers on this page if you have it printed out. 1. Use the following chart to calculate the value of / to use in the given optimization problem: A B C D E F G H I J K L M N O P R S T U V W X Y Z 1200 1300 1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 N = The number associated with the first letter of your first name N = For example: If my first name is Judy, I find J has the number 2200, so N = 2200 J= 220 0 Use Calculus to solve the following optimization problem: (8 points) Give both the exact solution, and the solution as a decimal, rounded to 2 decimal places. (Note: The exact solution does NOT need to be simplified.) A decorative, closed, rectangular box with a square base and top must have a volume of / cubic inches. The cost of materials to create the box is 90 cents per square inch for the bottom and sides, and $2.80 per square inch for the decorative top. What dimensions of the box will minimize the cost of materials to create the box? Verify that your answer gives the minimum value. (1 point)