15. Q15
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Similar Question 1
<p>Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximize profits, and raise <code class='latex inline'>\$1024</code>, if she sells the bottles for <code class='latex inline'>\$28</code> each. She also knows that she will lose <code class='latex inline'>\$4160</code> if she sells the bottles for only <code class='latex inline'>\$10</code> each.</p> <ul> <li>What selling price will ensure that she breaks even?</li> </ul>
Similar Question 2
<p>At the Mini Market, as the price of milk drops, sales increase. On an average day, a <code class='latex inline'>4</code>-L bag of milk costs $<code class='latex inline'>3.90</code>, and the store sells an average of <code class='latex inline'>120</code> bags. For each$<code class='latex inline'>0.10</code> reduction in price of a <code class='latex inline'>4</code>-L bag, sales increase by <code class='latex inline'>20</code> bags per day. The price and value of sales can be modelled as follows, where <code class='latex inline'>n</code> is the number of $<code class='latex inline'>0.10</code> price reductions.</p> <ul> <li>Price, in dollars: <code class='latex inline'>3.90-0.10n</code> </li> <li>Number of bags: <code class='latex inline'>120+20n</code> </li> </ul> <p>The total revenue is the product of the price and the number of bags sold. Find how many price reductions will result in revenue of$<code class='latex inline'>700</code>.</p>
Similar Question 3
<p>A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round-trip fare of $20. The operator estimates that for each$1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry?</p>
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Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>At the traffic safety bureau, Paul is conducting a study on the stoplights at a particular intersection. He determines that when there are <code class='latex inline'>18</code> green lights per hour, then, on average, <code class='latex inline'>12</code> cars can safely travel through the intersection on each green light. He also finds that if the number of green lights per hour increases by one, then one fewer car can travel through the intersection per light.</p><p>Determine a function to represent the total number of cars that will travel through the intersection for an increase of <code class='latex inline'>x</code> green light per hour.</p>
<p>A school has decided to sell T-shirts as a fundraiser. Research shows that <code class='latex inline'>800</code> students will buy one if they cost $<code class='latex inline'>5</code> each. For every <code class='latex inline'>50</code>¢ increase in the price, <code class='latex inline'>20</code> fewer students will buy T-shirts. What is the maximum revenue and for what price should the shirts sell?</p> <p>The number of hot dogs, <code class='latex inline'>n</code>, sold by Wayne’s Wiener World on a given day is modelled by <code class='latex inline'>n = 500 - 100p</code>, where <code class='latex inline'>p</code> is the price, in dollars.</p><p>Obtain an expression for the daily hot dog revenue when the revenue generated by hot dog sales is <code class='latex inline'>R = np</code>. </p> <p>An artisan can sell 120 garden ornaments per week at$4 per ornament. For each $0.50 decrease in price, he can sell 20 more ornaments.</p><p>a) Determine algebraic expressions for the price of a garden ornament and the number of ornaments sold.</p><p>b) Write an equation for the revenue using your expressions from part a).</p><p>c) Use your equation from part b) to find what price the artisan should charge to maximize revenue.</p> <p>At the Mini Market, as the price of milk drops, sales increase. On an average day, a <code class='latex inline'>4</code>-L bag of milk costs$<code class='latex inline'>3.90</code>, and the store sells an average of <code class='latex inline'>120</code> bags. For each $<code class='latex inline'>0.10</code> reduction in price of a <code class='latex inline'>4</code>-L bag, sales increase by <code class='latex inline'>20</code> bags per day. The price and value of sales can be modelled as follows, where <code class='latex inline'>n</code> is the number of$<code class='latex inline'>0.10</code> price reductions.</p> <ul> <li>Price, in dollars: <code class='latex inline'>3.90-0.10n</code> </li> <li>Number of bags: <code class='latex inline'>120+20n</code> </li> </ul> <p>The total revenue is the product of the price and the number of bags sold. Find how many price reductions will result in revenue of $<code class='latex inline'>700</code>.</p> <p>Maria produces and sells shell necklaces. The material for each necklace costs her$4. She has been selling them for $8 each and averaging sales of 40 per week. She has been told that she could charge more but has found that for each$0.50 increase in price, she would lose 4 sales each week. What selling price should she set and what would her profit per week be at this price?</p>
<p> A number of students charter a bus to go to a school football game at a total cost of <code class='latex inline'>\$80</code>. Eight of the students are ill and cannot go. Each of the remaining students then has to pay an extra <code class='latex inline'>50</code> cents. How many students go on the bus?</p> <p>The profit on the watches they sell is determined by the relation <code class='latex inline'>P = -2n^2 + 120n -1000</code>, where <code class='latex inline'>n</code> is the number of watches sold and <code class='latex inline'>P</code> is the profit in dollars.</p><p>a) What are the break-even points?</p><p>b) What is the maximum profit?</p> <p>The Sticker Warehouse sells rolls of stickers for$4.00 each. The average customer buys six rolls of stickers. The owner finds that, for every $0.25 decrease in price. the average customer buys an additional roll.</p><p>a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent The Sticker Warehouse&#39;s total revenue per customer.</p><p>b) With how many price reductions will the revenue per customer be$30?</p><p>c) What is the maximum predicted sales revenue per customer? With how many price reductions will this occur?</p>
<p>At the Mini Market, as the price of milk drops, sales increase. On an average day, a <code class='latex inline'>4</code>-L bag of milk costs $<code class='latex inline'>3.90</code>, and the store sells an average of <code class='latex inline'>120</code> bags. For each$<code class='latex inline'>0.10</code> reduction in price of a <code class='latex inline'>4</code>-L bag, sales increase by <code class='latex inline'>20</code> bags per day. The price and value of sales can be modelled as follows, where <code class='latex inline'>n</code> is the number of $<code class='latex inline'>0.10</code> price reductions.</p><p>Price, in dollars: <code class='latex inline'>3.90-0.10n</code> Number of bags: <code class='latex inline'>120+20n</code> </p><p>The total revenue is the product of the price and the number of bags sold. Find how many price reductions will result in revenue of$<code class='latex inline'>700</code>.</p>
<p>Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximize profits, and raise <code class='latex inline'>\$1024</code>, if she sells the bottles for <code class='latex inline'>\$28</code> each. She also knows that she will lose <code class='latex inline'>\$4160</code> if she sells the bottles for only <code class='latex inline'>\$10</code> each.</p> <ul> <li>What selling price will ensure that she breaks even?</li> </ul>
<p>A city transit system carries an average of 9450 people per day on its buses, at a fare of $1.75 each. The city wants to maximize the transit system’s revenue by increasing the fare. A survey shows that the number of riders will decrease by 210 for every$0.05 increase in the fare. What fare will result in the greatest revenue? How many daily riders will they lose at this new fare?</p>
<p>Tickets to a school dance cost $5, and the projected attendance is 300 people. For every$0.50 increase in the ticket price, the dance committee projects that attendance will decrease by 20. What ticket price will generate $1562.50 in revenue?</p> <p>Maria produces and sells shell necklaces. The material for each necklace costs her$4. She has been selling them for $8 each and averaging sales of 40 per week. She has been told that she could charge more but has found that for each$0.50 increase in price, she would lose 4 sales each week. What selling price should she set and what would her profit per week be at this price?</p>
<p>Emma sells her handmade jewellery at a local market. She has always sold her rings for <code class='latex inline'>\$10</code> each, but she is thinking about raising the price. Emma knows that her weekly revenue, <code class='latex inline'>r</code>, in dollars, is modelled by <code class='latex inline'>r=250+5n-2n^2</code>, where <code class='latex inline'>n</code> is the amount of rings she sold. Is it possible for Emma to earn <code class='latex inline'>\$500</code> in revenue? Explain.</p>
<p>A school has decided to sell T-shirts as a fundraiser. Research shows that <code class='latex inline'>800</code> students will buy one if they cost $<code class='latex inline'>5</code> each. For every <code class='latex inline'>50</code>¢ increase in the price, <code class='latex inline'>20</code> fewer students will buy T-shirts. What is the maximum revenue. and for What price should the shirts sell?</p> <p>A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for a round-trip fare of$20. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. What fare will maximize the number of people taking the ferry?</p> <p>Shelly sells photos of athletes to baseball, basketball, and hockey fans after their games. Her regular price is$10 per photograph, and she usually sells about 30 photographs. Shelly finds that, for each reduction in price of $0.50, she can sell an additional two photographs.</p><p>a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri’s total sales revenue.</p><p>b) At what price will Sherri’s revenue be$150?</p><p>c) At what price will her maximum revenue occur?</p><p>d) At what price will her revenue be $0?</p><p>e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)?</p> <p>An artisan can sell 120 garden ornaments per week at$4 per ornament. For each $0.50 decrease in price, he can sell 20 more ornaments.</p><p>a) Determine algebraic expressions for the price of a garden ornament and the number of ornaments sold.</p><p>b) Write an equation for the revenue using your expressions from part a).</p><p>c) Use your equation from part b) to find what price the artisan should charge to maximize revenue.</p> <p>Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximize profits of <code class='latex inline'>\$1024</code> if she sells the bottles for <code class='latex inline'>\$28</code> each. She also knows that she will lose <code class='latex inline'>\$4160</code> if she sells the bottles for only <code class='latex inline'>\$10</code> each.</p> <ul> <li>Write a quadratic relation to model her profit, <code class='latex inline'>P</code>, in dollars, if she sells the bottles for <code class='latex inline'>x</code> dollars each.</li> </ul> <p>Last year, a banquet hall charged <code class='latex inline'>\$30</code> per person, and <code class='latex inline'>60</code> people attended the hockey banquet dinner. This year, the hall&#39;s manager has said that if <code class='latex inline'>10</code> extra people that attend the banquet, they will decrease the price by $<code class='latex inline'>1.50</code> per person. What size group would maximize the profit for the hall this year?</p> <p>Shelly sells photos of athletes to baseball, basketball, and hockey fans after their games. Her regular price is$10 per photograph, and she usually sells about 30 photographs. Shelly finds that, for each reduction in price of $0.50, she can sell an additional two photographs.</p><p>a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri’s total sales revenue.</p><p>b) At what price will Sherri’s revenue be$150?</p><p>c) At what price will her maximum revenue occur?</p><p>d) At what price will her revenue be \$0?</p>
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