Decision tree diagrams
-
A decision tree is a quantitative method of tracing the outcomes of a decision so that the most profitable decision can be identified
-
Research-based estimates and probabilities are used to calculate likely outcomes
-
The net gain from a decision can be identified and used to consider whether an investment is worthwhile
-
-
Using decision trees provides several key advantages to the decision-making process:
-
Constructing a decision tree diagram may reveal options that haven’t previously been considered
-
Managers are forced to consider the risks associated with their choice, ahead of implementation
-
The quantitative approach requires deep research to be carried out
-
Decision tree diagrams
-
The key elements in a decision tree diagram are:
-
Decision points
-
Outcomes
-
Probabilities
-
Expected monetary values
-
A simple decision tree
-
Points where decisions need to be made are represented by squares
-
Square A represents the fact that a choice is required on opening a new store or expanding the website
-
-
Points where there are different outcomes are represented by circles called nodes
-
Circles B and C represent points at which the different options have a range of outcomes — success or failure
-
-
The probability or likelihood of each outcome is shown on the diagram
-
A certain outcome has a probability of 1
-
An impossible outcome has a probability of 0
-
Opening a new store has a 0.7 probability of success and a 0.3 probability of failure
-
Expanding the website has a 0.6 probability of success and a 0.4 probability of failure
-
-
-
The monetary value of each decision is based on the expected profit or loss of the outcome
-
If opening a new store is successful, a £420,000 profit is expected
-
If opening a new store is unsuccessful, a £24,000 loss is expected
-
If expanding the website is successful, a £480,000 profit is expected
-
If expanding the website is unsuccessful, a £32,000 loss is expected
-
Calculating expected monetary values
-
To compare the options, a business should take into account the expected values of each decision presented in the decision tree diagram
-
To calculate the expected monetary value of a decision, the following formula is used
(Expected value of success × probability) + (Expected value of failure × probability)
-
Using the example above, the expected value of opening a new store is
(£420,000 × 0.7) + (-£24,000 × 0.3)
= £294,000 + -£7,200
= £286,800
-
Using the example above, the expected value of expanding the website is
(£480,000 × 0.6) + (-£32,000 × 0.4)
= £288,000 + -£12,800
= £275,200
-
As the expected value of opening a new store is higher, at £286,800, than that of expanding the website, at £275,200, then, based purely on financial terms, the business should choose the option to open a new store
Worked Example
Caramelac is a lactose-free chocolate product manufactured by a large multinational confectionery business. In recent years, increased competition from other well-known brands has started to impact sales of the product, and managers are determined to maintain Caramelac’s market share.
Market research has shown that the business has two options:
a) Redevelop the product
b) Create a new advertising campaign
The expected outcomes and the probabilities of success and failure are shown in the decision tree below.
Calculate the expected values of each option and decide, on financial grounds, which option Caramelac’s brand managers should choose.
[6]
Step 1: Calculate the expected value of redeveloping the product
<img alt=”equals space left parenthesis £ 840 comma 000 space cross times space 0.5 right parenthesis space plus space left parenthesis negative £ 84 comma 000 space cross times space 0.5 right parenthesis space equals space £ 420 comma 000 space equals space £ 420 comma 000 space plus negative £ 42 comma 000 space space equals space £ 378 comma 000 space” data-mathml=”<math ><semantics><mrow><mo>=</mo><mo> </mo><mo>(</mo><mo>£</mo><mn>840</mn><mo>,</mo><mn>000</mn><mo> </mo><mo>×</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo> </mo><mo>+</mo><mo> </mo><mo>(</mo><mo>-</mo><mo>£</mo><mn>84</mn><mo>,</mo><mn>000</mn><mo> </mo><mo>×</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>£</mo><mn>420</mn><mo>,</mo><mn>000</mn><mo> </mo><mspace linebreak=”newline”/><mspace linebreak=”newline”/><mo>=</mo><mo> </mo><mo>£</mo><mn>420</mn><mo>,</mo><mn>000</mn><mo> </mo><mo>+</mo><mo>-</mo><mo>£</mo><mn>42</mn><mo>,</mo><mn>000</mn><mo> </mo><mo> </mo><mspace linebreak=”newline”/><mspace linebreak=”newline”/><mo>=</mo><mo> </mo><mo>£</mo><mn>378</mn><mo>,</mo><mn>000</mn><mo> </mo></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”116″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%22116%22%20width%3D%22420%22%20wrs%3Abaseline%3D%2257%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E(%3C%2Fmo%3E%3Cmo%3E%26%23xA3%3B%3C%2Fmo%3E%3Cmn%3E840%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E000%3C%2Fmn%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E)%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E(%3C%2Fmo%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmo%3E%26%23xA3%3B%3C%2Fmo%3E%3Cmn%3E84%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E000%3C%2Fmn%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E.%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmo%3E)%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA3%3B%3C%2Fmo%3E%3Cmn%3E420%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E000%3C%2Fmn%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA3%3B%3C%2Fmo%3E%3Cmn%3E420%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E000%3C%2Fmn%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmo%3E%26%23xA3%3B%3C%2Fmo%3E%3Cmn%3E42%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E000%3C%2Fmn%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA3%3B%3C%2Fmo%3E%3Cmn%3E378%3C%2Fmn%3E%3Cmo%3E%2C%3C%2Fmo%3E%3Cmn%3E000%3C%2Fmn%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math19286848d8038890add09da7c02’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAAFxjdnQgDVUNBwAAAXgAAAA6Z2x5ZoPi2VsAAAG0AAACVGhlYWQQC2qxAAAECAAAADZoaGVhCGsXSAAABEAAAAAkaG10eE2rRkcAAARkAAAAHGxvY2EAHTwYAAAEgAAAACBtYXhwBT0FPgAABKAAAAAgbmFtZaBxlY4AAATAAAABn3Bvc3QB9wD6AAAGYAAAACBwcmVwa1uragAABoAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEAEgAAAAOAAgAAgAGACsALAAuAD0A1yIS%2F%2F8AAAArACwALgA9ANciEv%2F%2F%2F9b%2F1v%2FV%2F8f%2FLt30AAEAAAAAAAAAAAAAAAAAAAAAAVQDLACAAQAAVgAqAlgCHgEOASwCLABaAYACgACgANQAgAAAAAAAAAArAFUAgACrANUBAAErAAcAAAACAFUAAAMAA6sAAwAHAAAzESERJSERIVUCq%2F2rAgD%2BAAOr%2FFVVAwAAAQCAAFUC1QKrAAsASQEYsgwBARQTELEAA%2FaxAQT1sAo8sQMF9bAIPLEFBPWwBjyxDQPmALEAABMQsQEG5LEBARMQsAU8sQME5bELBfWwBzyxCQTlMTATIREzESEVIREjESGAAQBVAQD%2FAFX%2FAAGrAQD%2FAFb%2FAAEAAAEAVf9kANUAgAAKAAAzNTMVFAYHJz4BN1WALy8bHh4BgHo9URQpDjQxAAEAIAAAAKAAgAADAC8YAbAEELAD1LADELAC1LADELAAPLACELABPACwBBCwA9SwAxCwAjywABCwATwwMTczFSMggICAgAACAIAA6wLVAhUAAwAHAGUYAbAIELAG1LAGELAF1LAIELAB1LABELAA1LAGELAHPLAFELAEPLABELACPLAAELADPACwCBCwBtSwBhCwB9SwBxCwAdSwARCwAtSwBhCwBTywBxCwBDywARCwADywAhCwAzwxMBMhNSEdASE1gAJV%2FasCVQHAVdVVVQACAIAAVQLVAoAAAwAHAEYYsAEUALEAABMQsQAJ5LEAARMQsAQ8sQYI9LACPDABsQgBExCxAAP2sAc8sQEF9bAGPLIFBwAQ9LACPLEJA%2BaxBAX1sAM8EzMBIxEzASOAVQIAVVX%2BAFUCgP3VAiv91QABAIABVQLVAasAAwAwGAGwBBCxAAP2sAM8sQIH9bABPLEFA%2BYAsQAAExCxAAblsQABExCwATyxAwX1sAI8EyEVIYACVf2rAatWAAEAAAABAADVeM5BXw889QADBAD%2F%2F%2F%2F%2F1joTc%2F%2F%2F%2F%2F%2FWOhNzAAD%2FIASAA6sAAAAKAAIAAQAAAAAAAQAAA%2Bj%2FagAAF3AAAP%2B2BIAAAQAAAAAAAAAAAAAAAAAAAAcDUgBVA1YAgAEzAFUAyAAgA1YAgANWAIADVgCAAAAAAAAAACgAAAChAAAAywAAAREAAAGbAAACCgAAAlQAAQAAAAcAXgAFAAAAAAACAIAEAAAAAAAEAADeAAAAAAAAABUBAgAAAAAAAAABABIAAAAAAAAAAAACAA4AEgAAAAAAAAADADAAIAAAAAAAAAAEABIAUAAAAAAAAAAFABYAYgAAAAAAAAAGAAkAeAAAAAAAAAAIABwAgQABAAAAAAABABIAAAABAAAAAAACAA4AEgABAAAAAAADADAAIAABAAAAAAAEABIAUAABAAAAAAAFABYAYgABAAAAAAAGAAkAeAABAAAAAAAIABwAgQADAAEECQABABIAAAADAAEECQACAA4AEgADAAEECQADADAAIAADAAEECQAEABIAUAADAAEECQAFABYAYgADAAEECQAGAAkAeAADAAEECQAIABwAgQBNAGEAdABoACAARgBvAG4AdABSAGUAZwB1AGwAYQByAE0AYQB0AGgAcwAgAEYAbwByACAATQBvAHIAZQAgAE0AYQB0AGgAIABGAG8AbgB0AE0AYQB0AGgAIABGAG8AbgB0AFYAZQByAHMAaQBvAG4AIAAxAC4AME1hdGhfRm9udABNAGEAdABoAHMAIABGAG8AcgAgAE0AbwByAGUAAAMAAAAAAAAB9AD6AAAAAAAAAAAAAAAAAAAAAAAAAAC5BxEAAI2FGACyAAAAFRQTsQABPw%3D%3D)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%40font-face%7Bfont-family%3A’round_brackets18549f92a457f2409’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMjwHLFQAAADMAAAATmNtYXDf7xCrAAABHAAAADxjdnQgBAkDLgAAAVgAAAASZ2x5ZmAOz2cAAAFsAAABJGhlYWQOKih8AAACkAAAADZoaGVhCvgVwgAAAsgAAAAkaG10eCA6AAIAAALsAAAADGxvY2EAAARLAAAC%2BAAAABBtYXhwBIgEWQAAAwgAAAAgbmFtZXHR30MAAAMoAAACOXBvc3QDogHPAAAFZAAAACBwcmVwupWEAAAABYQAAAAHAAAGcgGQAAUAAAgACAAAAAAACAAIAAAAAAAAAQIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAo8AMGe%2F57AAAHPgGyAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACACgAKf%2F%2FAAAAKAAp%2F%2F%2F%2F2f%2FZAAEAAAAAAAAAAAFUAFYBAAAsAKgDgAAyAAcAAAACAAAAKgDVA1UAAwAHAAA1MxEjEyMRM9XVq4CAKgMr%2FQAC1QABAAD%2B0AIgBtAACQBNGAGwChCwA9SwAxCwAtSwChCwBdSwBRCwANSwAxCwBzywAhCwCDwAsAoQsAPUsAMQsAfUsAoQsAXUsAoQsADUsAMQsAI8sAcQsAg8MTAREAEzABEQASMAAZCQ%2FnABkJD%2BcALQ%2FZD%2BcAGQAnACcAGQ%2FnAAAQAA%2FtACIAbQAAkATRgBsAoQsAPUsAMQsALUsAoQsAXUsAUQsADUsAMQsAc8sAIQsAg8ALAKELAD1LADELAH1LAKELAF1LAKELAA1LADELACPLAHELAIPDEwARABIwAREAEzAAIg%2FnCQAZD%2BcJABkALQ%2FZD%2BcAGQAnACcAGQ%2FnAAAQAAAAEAAPW2NYFfDzz1AAMIAP%2F%2F%2F%2F%2FVre7u%2F%2F%2F%2F%2F9Wt7u4AAP7QA7cG0AAAAAoAAgABAAAAAAABAAAHPv5OAAAXcAAA%2F%2F4DtwABAAAAAAAAAAAAAAAAAAAAAwDVAAACIAAAAiAAAAAAAAAAAAAkAAAAowAAASQAAQAAAAMACgACAAAAAAACAIAEAAAAAAAEAABNAAAAAAAAABUBAgAAAAAAAAABAD4AAAAAAAAAAAACAA4APgAAAAAAAAADAFwATAAAAAAAAAAEAD4AqAAAAAAAAAAFABYA5gAAAAAAAAAGAB8A%2FAAAAAAAAAAIABwBGwABAAAAAAABAD4AAAABAAAAAAACAA4APgABAAAAAAADAFwATAABAAAAAAAEAD4AqAABAAAAAAAFABYA5gABAAAAAAAGAB8A%2FAABAAAAAAAIABwBGwADAAEECQABAD4AAAADAAEECQACAA4APgADAAEECQADAFwATAADAAEECQAEAD4AqAADAAEECQAFABYA5gADAAEECQAGAB8A%2FAADAAEECQAIABwBGwBSAG8AdQBuAGQAIABiAHIAYQBjAGsAZQB0AHMAIAB3AGkAdABoACAAYQBzAGMAZQBuAHQAIAAxADgANQA0AFIAZQBnAHUAbABhAHIATQBhAHQAaABzACAARgBvAHIAIABNAG8AcgBlACAAUgBvAHUAbgBkACAAYgByAGEAYwBrAGUAdABzACAAdwBpAHQAaAAgAGEAcwBjAGUAbgB0ACAAMQA4ADUANABSAG8AdQBuAGQAIABiAHIAYQBjAGsAZQB0AHMAIAB3AGkAdABoACAAYQBzAGMAZQBuAHQAIAAxADgANQA0AFYAZQByAHMAaQBvAG4AIAAyAC4AMFJvdW5kX2JyYWNrZXRzX3dpdGhfYXNjZW50XzE4NTQATQBhAHQAaABzACAARgBvAHIAIABNAG8AcgBlAAAAAAMAAAAAAAADnwHPAAAAAAAAAAAAAAAAAAAAAAAAAAC5B%2F8AAY2FAA%3D%3D)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%228.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22round_brackets18549f92a457f2409%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%2224.5%22%20y%3D%2216%22%3E(%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%2233.5%22%20y%3D%2216%22%3E%26%23xA3%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%2253.5%22%20y%3D%2216%22%3E840%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E000%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22111.5%22%20y%3D%2216%22%3E%26%23xD7%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22128.5%22%20y%3D%2216%22%3E0%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22135.5%22%20y%3D%2216%22%3E.%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22142.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Ctext%20font-family%3D%22round_brackets18549f92a457f2409%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22149.5%22%20y%3D%2216%22%3E)%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22165.5%22%20y%3D%2216%22%3E%2B%3C%2Ftext%3E%3Ctext%20font-family%3D%22round_brackets18549f92a457f2409%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22181.5%22%20y%3D%2216%22%3E(%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22192.5%22%20y%3D%2216%22%3E%26%23×2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22207.5%22%20y%3D%2216%22%3E%26%23xA3%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22223.5%22%20y%3D%2216%22%3E84%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22234.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22250.5%22%20y%3D%2216%22%3E000%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22276.5%22%20y%3D%2216%22%3E%26%23xD7%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22293.5%22%20y%3D%2216%22%3E0%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22300.5%22%20y%3D%2216%22%3E.%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22307.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Ctext%20font-family%3D%22round_brackets18549f92a457f2409%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22314.5%22%20y%3D%2216%22%3E)%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22330.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22349.5%22%20y%3D%2216%22%3E%26%23xA3%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20text-anchor%3D%22middle%22%20x%3D%22369.5%22%20y%3D%2216%22%3E420%3C%2Ftext%3E%3Ctext%20font-family%3D%22math19286848d8038890add09da7c02%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3
Responses