Pretend you own a company that sells items over the Internet. You decide that shipping costs will be based on the total weight of a customer's purchase. Write a piecewise function for your shipping charges. Include from three to five weight intervals. Post your store name, briefly describe the types of items you sell (for example, pet toys), and give a description of your shippingcharge function (clearly state the rules, and the domain intervals to which they apply). Answer the following: A. Is your shippingcharge function a step function? If yes, look on the discussion board for a student who did not write a step function. If everyone wrote a step function, discuss how shipping charges could be determined by using a piecewise function that is not a step function. Describe pros and cons of using each type of function to determine shipping costs. B. Find a store on the board, other than your own, and pretend you are making a purchase from their website. The package of goods they are shipping to you weighs 25 pounds. Determine the shipping charges. Confirm the charges with the store owner. C. Which store charges the most for shipping a 25pound package? Which store charges the least? D. How are the domains and ranges of all the shippingcharge functions similar? How are they different? E. Other than by total weight, how else can shipping charges be determined? This question below belongs to another student, so you can provide nformation fot questions B,C, D, E Stylish shoes I sell all types of footwear from all different types of designers and sizes. I charge a regular rate of $2 on a 3 weight order, and then $.25 for every half pound following that. However, there is a maximum weight limit of 25 pounds on an order because we do not have the capacity to send more than 25 pounds. a) y=.25x + 2 (x>3) , y=13.5 (x<25) b)c)d) e) shipping charges can be charged by the amount of distance the company has to send the package. It also depends on how quickly the consumer needs the package. Let weight of each item = x and the cost of each item be given as f(x) Therefore the piecewise function for shipping charges is given as ; f(x) = { x+100 1x 10 2x+500 10x 20 4x+1000 20 x 30 6x+1500 30x40 8x+2000 x40 Name of Store : Hedge Office and School Suppliers Items: 1.Black office chair: Features include: Padded seat and lack all-day comfort Pneumatic seat height adjustment 230-pound maximum weight capacity Measure 24.9 inches deep by 23.8 inches wide 2.Stand-alone photo scanner. Features: Simple, standalone and lets you scan paper anywhere in your office Scans full color photos in 9 seconds 3.Epson Business Printer Features High print quality and excellent colors Measures 8.7inches high, 15.4 inches wide and 14.6 inches deep when fully open Power code, USB cable, telephone code and paper included Takes 4-ink cartridges, magenta, cyan and yellow 4.Light-touch Paper Punch Punches from 2 to 5 holes, 25 sheet paper capacity Requires 40% less manual punching energy Easily removable spill resistant chip tray Description of shipping charge function Here , x is the weight of item, 100 is a constant factor representing custom duties for shipping. This function represents the cost of shipping of an item that has a weight given by the interval 1x 10. The shipping price increases by a factor of 2 (operation cost of stocking the item) for an increase in range of 10. f(x) = { x+100 1 x 10 operation cost, factor of 1, custom duties = 100 2x+500 10 x 20 operation cost is factor of 2, custom duties = 500 4x+1000 20 x 30 operation cost is factor of 4, custom duties = 1000 6x+1500 30 x40 operation cost is factor of 6, custom duties = 1500 8x+2000 x40 operation cost is factor of 8, custom duties = 2000 , x is the weight of item, 100 is a constant factor representing custom duties for shipping. This function represents the cost of shipping of an item that has a weight given by the interval 1x 10. The shipping price increases by a factor of 2 (operation cost of stocking the item) for an increase in range of 10. Part A This is a step function, it contains constant pieces which as they change from one interval to another. (Advantages)Pros of Step functions It utilizes open circles and points on graph hence can be used to show trend It shows horizontal pieces on the graph hence gives an insight of shipping cost with change in domain Disadvantages (Cons) It is discontinuous and therefore cannot show the price change trend continuously It may or may not be necessarily a function which might make it difficult to determine the factors affecting shipping cost. Shipping charges can be determine without using step function by using absolute define function such as f(x) = { x + 100 x 10 -x +100 x 10 Advantages of absolute defined functions: The range increase for zero to infinity hence cannot be used to determine shipping cost for weights below the interval Average rate of change is constant in each straight-line section of the graph which shows the trend of shipping cost versus weight Absolute/relative minimum is zero Disadvantages (Cons) The function decrease from zero to negative infinity as x tends to lower numbers It is symmetric about x=10, implying that the cost is independent of operation costs. Average rate of change is constant in each straight-line section of the graph. Part B, C ,D I CAN'T SEE THE DISCUSSION BOARD (YOU DIDN'T PROVIDE IT) TO FIND A STORE AND COMPARE THE VALUES , BUT ONCE YOU CHOOSE A STORE USE THE ABOVE EQUATION TO ESTIMATE THE SHIPPING PRICE. YOU CAN AS WELL PROVIDE THE VALUES SO I COMPLETE THIS PART Part E Other ways of determining shipping price: Dimensions of the item such as length, breadth and height to determine the floor space the item will occupy Nature of the item: Delicate items such as computers or glassware could be used to determine shipping cost in terms of urgency and method of shipping to be used which will be reflected in the shipping price. Distance: Shipping price can be determine by factoring in the distance the item has to be taken so as to determine duration of shipment and risks costs