Question 486382: A floor salesman was asked to help Mrs. Cooper with a problem situation. She wanted to remove the carpet in her den and replace it with green marble, 9 inch square tiles. The rectangular room measures 12 feet by 15 feet.
A. What is the main question (s) that you think the floor salesman is being asked
by Mrs. Cooper?
B. Identify at least two facts in the problem statement that are not relevant to finding the solution to this problem.
C. Name at least three contextual or mathematical clues that the floor salesman will have to use to interpret this problem situation.
D. To clarify his thinking, what questions will the salesman have to consider before answering the question being posed?
E. What additional information will the floor salesman need to resolve the problem situation?
F. What mathematical models or formulas will the floor salesman have to use to determine the solution to this problem?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! This is a very interesting situation. It sounds as if this problem were designed by either a mathematician or an educator who never has had one day of practical experience as a salesman, especially as a flooring salesman. Let's discuss a little bit each of the six questions (A through F) that you have been presented with.
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Question A. What is the main question(s) that you think the floor salesman is being asked by Mrs. Cooper?
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Unless Mrs. Cooper is a woman to whom a dollar (or hundreds or thousands of dollars) is of little concern, I can guarantee that the primary question she has starts with, "How much will it cost me to ...?" If she is astute, she also will ask questions about durability of marble tile, what work or cost is required to maintain it, how long can be expected to last, and how much of the cost of this job could she expect to recapture if she later decided to sell the house? She may also want to know if she can save money by switching from 9" square tiles to 12" squares or 18" squares or some other dimensions. She may want to know if the green color is difficult to find. If she is an environmentalist, she may ask where the marble is being quarried in search of the nearest source that does not involve the environmental impact of long distance transportation. For example, does the tile that she is specifying need to be imported from a great distance away. She may ask to see actual samples of the marble. She may ask if the tile is gauged and calibrated (of uniform thickness at the edges and flat across the back side as well as on the upward face). She may ask if the salesman would recommend a highly polished exposed side. In addition, Mrs. Cooper may want to know how long it will take to gather all the supplies and to schedule the work as well as how long the actual work in her house can be expected to last. She might ask how much dirt or dust can she expect from the installation process and how the installers will help to minimize that nuisance. (Wait until she sees the dust involved with wet sawing or grinding marble tile.) Many other questions are likely to arise as she talks to the salesman.
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Question B. Identify at least two facts in the problem statement that are not relevant to finding the solution to this problem.
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To the salesman, every statement in the problem is relevant to finding a solution. For example, even the fact that the customer's name is Mrs. Cooper is relevant. If he called her Mrs. Smith or Miss Jones or "honey" or something else inappropriate, he is well on his way to losing a sale. (If she's done her homework, she may even know more about the job than the salesman does. Just ask a Home Depot or Lowe's clerk detailed questions about floor tile.) The fact that the room is a den is important because it will give the salesman a clue of what type of traffic the floor is likely to experience. The color green is important because it may well determine how available such tiles are and where the quarry is. The fact that Mrs. Cooper has asked for 9" square tiles is germane since that is not a common size. Therefore, this size may require a special order which will add to cost, time, and availability. (Common sizes are 3" x 6", 4" x 8", 8" x 8", 12" x 12", 18" x 18", 16" x 24".) The fact that marble is replacing carpet is also important. If the marble tile (usually 3/8" but may be 1/2" thick) is not as thick as the carpet and pad that currently are on the floor, the removal of the carpet can create a height difference with the baseboard around the room and with the existing door jamb casement as well.
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The salesman is in a battle with his competition to prove to the customer that he is the one she should trust because he is thorough, knowledgeable, a person who caters to her need for flooring and what she wants, and is presenting a quality solution that is cost competitive. He also needs to give her confidence that the product he is selling to her will be a credit to the appearance of her house and to her taste in decorating. He also needs to know and understand the impact of everything involved so that he can sure all the costs are appropriately identified and managed.
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Question C. Name at least three contextual or mathematical clues that the floor salesman will have to use to interpret this problem situation.
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Since it is very basic to the fundamental cost of the project, the salesman needs to determine if Mrs. Cooper really means marble tile or whether she might be using marble as a generic term for any natural stone tile (slate, granite, marble, sandstone, travertine, limestone, etc.) or maybe even for ceramic, glazed clay, glass, or other man-made tiles. The exact type of tile will impact the materials cost. Really good marble tile is expensive. Some is in the vicinity of $20 US per square foot and for this job (requiring approximately 200 square feet of tile as discussed below) the cost of the tile will be $4000 US before adding costs for all the other materials, as well as labor, and miscellaneous expenses.
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Obviously the square footage of the floor (12' x 15' = 180 sq ft) is important as a clue. So is the fact that Mrs. Cooper has asked for 9" square tiles since the size of the tiles will help determine how many are needed to cover the floor. (However, marble floor tile is generally priced in terms of square feet, not in terms of tile count.) Not implicitly stated in the problem is the width of the grout spaces that Mrs. Cooper would like between tiles. This has an impact because the wider the grout lines, the more the grout mix and labor will be affected. The narrower the grout lines, the more floor space that the marble tile itself will have to cover with an accompanying reduction in the amount of grout mix required. Also, not covered will be the excess tile that will be required in case a tile breaks or is cut wrong. Although the tile is to cover the 180 square feet of the den, the salesman (if he is smart) will probably add about 10% overage to cover such unforeseen contingencies, to allow for throwaway material along room edges where only half tiles may be needed, and to give spares to the customer in case in the future a tile cracks or is stained and needs to be replaced. Replacement tiles should be from the same quarry and lot so that they match the damaged tiles. So although the salesman is to cover 180 square feet with tile, his likely order will be for approximately 200 square feet of tile.
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The salesman also needs to recognize the problems associated with installing tile. A carpet and its pad can cover and disguise a multitude of sins in the sub floor. Marble tile is not so forgiving. Because it usually has a polished surface, if all the tiles are not cemented down nearly uniformly flat, the ambient light will reflect differently from each tile and will make the floor look like it was haphazardly installed. This may make it necessary to level the tile sub flooring, and that would have to be factored into the mathematical calculations for cost and materials. The salesman has to understand the labor requirements such as number of team members, the hourly cost rate (including insurance and benefits) for each type of laborer involved, the expected duration of the job, material costs (for example tile, tile adhesive, sub floor treatments, grout, tool wear and tear, etc.), and hidden costs such as transportation to/from the job site.
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Question D. To clarify his thinking, what questions will the salesman have to consider before answering the question being posed?
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The previous discussion above has already identified some of the factors/questions that the salesman will have to consider before answering Mrs. Cooper's question about what will it cost. In addition the salesman will also need to determine the scope of the work to be performed. For example, will the installers be responsible for removing the existing carpet and pad and for disposing of it? Will the installation include any modifications to the baseboard situation to disguise any gaps that may be encountered as a result of the difference in the height of the carpet and pad as compared to the height of tile? Will the old baseboard have to be removed and replaced so that it matches the new height of the tile flooring? Will transitions have to be installed so the new flooring in the den will mate well with the existing flooring just outside the doors leading into the den?
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Question E. What additional information will the floor salesman need to resolve the problem situation?
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A lot of the discussion above relates to what the salesman needs to evaluate and resolve in order to price the job so that he stays in contention with the competition. On the other hand, he must price the job so it covers costs and contingency costs plus some profit for the company he represents.
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Question F. What mathematical models or formulas will the floor salesman have to use to determine the solution to this problem?
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Obviously, the mathematical model must consider the area of floor to be installed in the room. We've also recognized that this model will also likely include the cost of a 10% overage in the amount of tile to provide for contingencies and spares for potential future damage. The width of the grout between tiles is a factor that can be determined and priced.
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However, salesmen often have other models that affect the cost being proposed to the customer. For example, the salesman may say that in his experience, the average cost of materials represents 1/3 of the total cost and the cost of labor and other miscellaneous associated costs represents 2/3 of the total cost. Therefore, if he carefully estimates and computes the cost of the materials (call that cost M), he can say that 1/3 of the total cost of the job (call it C) can be computed from the equation:
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Multiplying both sides of this equation by 3 results in:
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So if he closely prices the material costs (M) he can get the cost to perform the entire job (C) by multiplying the material costs by 3. Then he can compute the labor and other miscellaneous costs as being be two-thirds of C.
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Other costs to the customer must be added to that amount. For example, if he wants the job to have a 10% profitability he needs to add 10% of C to the total cost to the customer. He also needs to add to the customer's bill any taxes that must be paid. For example, sales taxes that must be paid on the materials.
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Hopefully, this rambling, unproofread discussion will be of some help to you and will give you ideas of how to answer the questions posed by this problem. Feel free to modify the organization of your answers.
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Obviously real life is often considerably different from and more complex than what the educators and mathematicians think while designing problems meant to teach lessons. Might as well get used to it because that's the way that life is, and that's what makes life so really interesting as you travel through it.
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