8 Logical Funclions and Selection Structures Problems 309 30 8.13 Suppose the following matrix represents the number of saws ordered from your company cach month over the last year. (b) Write a program that prompts the user to enter one of the following: triangle saws = (1,4,5,3,7,5,3,10,12,8, 7, 4] square pentagon hexagon Use the input to define the value of n via a switch/case structure; then use n to calculate the sum of the interior angles in the figure. All the numbers should be zero or positive. (a) Use an if statement to check whether any of the values in the matrix are invalid. (Evaluate the whole matrix at once in a single if state- ment.) Send the message "All valid" or else “Invalid number ſound" to the screen, depending on the results of your analysis. (b) Change the saws matrix to include at least one negative number, and check your program to make sure that it works for both cases. 8.14 Most large companies encourage employees to save by matching their con- tributions to a 401 (k) plan. The government limits how much you can save in these plans, because they shelter income from taxes until the money is withdrawn during your retirement. The amount you can save is tied to your income, as is the amount your employer can contribute. The government will allow you to save additional amounts without the tax benefit. These plans change from year to year, so this example is just a made-up "what if." Suppose the Quality Widget Company has the savings plan described in Table 8.10. Create a function that finds the total yearly contribution to your savings plan, based on your salary and the percentage you contribute. Remember, the total contribution consists of the employee contribution and the company contribution. (c) Reformulate your program from part (b) so that it uses a menu. 8.16 At a local university, each engineering major requires a different number of credits for graduation. For example, recently the requirements were as follows: Civil Engineering Chemical Engineering Computer Engineering Electrical Engineering Mechanical Engineering 130 130 122 126.5 129 Prompt the user to select an engineering program from a menu. Use a switch/case structure to send the minimum number of credits required for graduation back to the command window. 8.17 The easiest way to draw a star in MATLAB® is to use polar coordinates. You simply need to identify points on the circumference of a circle and draw lines between those points. For example, to draw a five-pointed star, start at the top of the circle (0 = 7/2, r 1) and work counterclockwise (Figure P8.17). Prompt the user to specify either a five-pointed or a six-pointed star, using a menu. Then create the star in a MATLAB® figure window. Note that a six-pointed star is made of three triangles and requires a strategy diſferent from that used to create a five-pointed star. Table 8.10 Quality Widget Company Savings Plan Maximum You Can Save Tax Free Maximum the Company Will Match Income Up to $30,000 10% 10% Between $30,000 and 10% $60,000 10% of the first $30,000 and 5% of the amount above $30,000 Switch, ifclsc Between $60,000 and 10% of the first $60,000 and 8% $100,000 10% of the first $30,000 and 5% of the amount between $30,000 and $60,000; nothing for the remainder above $60,000 CHALLENGE PROBLEMS of the amount above $60,000 8.18 Most major airports have separate lots for long-term and short-term parking. The cost to park depends on the lot you select, and how long you stay. Consider this rate structure from the Salt Lake International Airport during 10% of the first $60,000 and 8% of the amount between $60,000 and $100,000; nothing on the amount above $100,000 Nothing-highly compensaled employees are exempt from this plan and participate in stock options instead Above $100,000 the summer of 2008. • Long-Term (Economy) Parking • The first hour is $1.00, and each additional hour or fraction thereof is $1.00 Daily maximum $6.00 • Weekly maximum $42.00 • Short-Term Parking • The first 30 minutes are free and each additional 20 minutes or fraction thereof is $1.00 • Daily maximum $25.00 SWITCH/CASE 8.15 In order to have a closed geometric figure composed of straight lines (Figure P8.15), the angles in the figure must add to (n – 2) (180 degrees) where n is the number of sides. Write a program that asks the user the following: Figure P8.15 Regular Polygons. (a) Prove this statement to yourself by creating a vector called n from 3 to 6 and calculating the angle sum from the formula. Compare what you know about geometry with your answer. • Which lot are you using? • How many wecks, hours, days, and minutes did you park? Your should then calculate the parking bill. program