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Marketing & Business Operations: Problem Solving with Exponents & Staffing, Study notes of Marketing

An explanation of the order of operations concept, its importance in marketing and business, and how to use it to predict staffing and product needs. It includes examples, formulas, and problem-solving strategies. Students will learn how to apply and extend the properties of exponents to solve problems with rational exponents and use the order of operations model to evaluate staffing and supply needs.

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2021/2022

Uploaded on 09/12/2022

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Sales, Distribution, and Marketing Operations (52.1801) T-Chart
Originated June 2011 CC.2.1.HS.F.1 Reviewed June 2015 1
Use prediction models
=
Apply and extend the properties of exponents to solve
problems with rational exponents
Program Task: Students will correctly staff and supply
needs using the Order of Operation Business model.
PA Core Standard: CC.2.1.HS.F.1
Description: Apply and extend the properties of exponents to solve
problems with rational exponents.
Program Associated Vocabulary:
FORMULA, ORDER OF OPERATIONS
Math Associated Vocabulary:
SIMPLIFY NUMERICAL EXPRESSION, TERM
Program Formulas and Procedures:
Understanding how to use the Order of Operations is an
important tool for managers to use in the field of marketing
and business. Using the Order of Operations model as a
tool to predict the proper amount of supplies needed to
operate a business is crucial to the success of a business.
The proper application of this concept can help a manager
evaluate the staffing needs of the business as well as the
supply needs of the business that manufactures products for
resale.
Example:
A concession vendor at Coca Cola Par needs to know
how much bottled water to order for Saturday’s home game.
The weather forecast for Saturday’s game is a high
temperature of 80 degrees. The park presold 2000 tickets.
Calculate the number of bottles of water to order. The
prediction formula for this scenario is:
w = (.1(a 65))2 x 1.05b + 500
a = Predicted High Temp
b = Presold Tickets
w = number of bottles of water to order
Solution:
First, substitute in the given information:
a = 80
b = 2000
w = (.1(80 65))2 x 1.05(2000) +500
Next, solve the problem using the order of operations:
w = (.1(15))2 x 2100 + 500
w = (1.5)2 x 2100 + 500
w = 2.25 x 2100 + 500
w = 4725 + 500
w = 5225
If the temperature is predicted to be 80 degrees and the
presold ticket amount is 2000, the concession vendor should
order 5225 bottles of water for the game on Saturday.
Formulas and Procedures:
P
Do all operations in PARENTHESIS. Start with the
innermost set.
E
Evaluate all EXPONENTS.
M
Do MULTIPLICATION and DIVISION in order
from left to right.
D
A
Do ADDITION and SUBTRACTION in order from
left to right.
S
One way to remember the order of operations is:
Please Excuse My Dear Aunt Sally.
Remembering that my and dear go together since they both describe
Aunt Sally who is one person.
Example:
(7 + 3)2 - 21÷7 + 10(2) =
102 - 21÷7 + 10(2) Parentheses
100 - 21÷7 + 10(2) Exponents
100 3 +20 Multiplication and Division
97 + 20 Addition and Subtraction
= 117
pf3
pf4

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Use prediction models = Apply and extend the properties of exponents to solve problems with rational exponents Program Task: Students will correctly staff and supply needs using the Order of Operation Business model. PA Core Standard: CC.2.1.HS.F. 1 Description: Apply and extend the properties of exponents to solve problems with rational exponents. Program Associated Vocabulary: FORMULA, ORDER OF OPERATIONS Math Associated Vocabulary: SIMPLIFY NUMERICAL EXPRESSION, TERM Program Formulas and Procedures: Understanding how to use the Order of Operations is an important tool for managers to use in the field of marketing and business. Using the Order of Operations model as a tool to predict the proper amount of supplies needed to operate a business is crucial to the success of a business. The proper application of this concept can help a manager evaluate the staffing needs of the business as well as the supply needs of the business that manufactures products for resale. Example: A concession vendor at Coca Cola Park® needs to know how much bottled water to order for Saturday’s home game. The weather forecast for Saturday’s game is a high temperature of 80 degrees. The park presold 2000 tickets. Calculate the number of bottles of water to order. The prediction formula for this scenario is: w = (.1(a – 65))^2 x 1.05b + 500 a = Predicted High Temp b = Presold Tickets w = number of bottles of water to order Solution: First, substitute in the given information: a = 80 b = 2000 w = (.1(80 – 65))^2 x 1.05(2000) + Next, solve the problem using the order of operations: w = (.1(15))^2 x 2100 + 500 w = (1.5)^2 x 2100 + 500 w = 2.25 x 2100 + 500 w = 4725 + 500 w = 5225 If the temperature is predicted to be 80 degrees and the presold ticket amount is 2000, the concession vendor should order 5225 bottles of water for the game on Saturday. Formulas and Procedures:

P

Do all operations in PARENTHESIS. Start with the innermost set.

E Evaluate all^ EXPONENTS.

M Do MULTIPLICATION and DIVISION in order

from left to right.

D

A Do ADDITION and SUBTRACTION in order from

left to right.

S

One way to remember the order of operations is: P lease E xcuse M y D ear A unt S ally. Remembering that my and dear go together since they both describe Aunt Sally who is one person. Example: (7 + 3)^2 - 21÷7 + 10(2) = 102 - 21÷7 + 10(2) Parentheses 100 - 21÷7 + 10(2) Exponents 100 – 3 +20 Multiplication and Division 97 + 20 Addition and Subtraction = 117

Instructor’s Script - Comparing and Contrasting Order of Operations is an essential skill for any student in a technical area that uses formulas. In addition to substituting values into the formula, the student must also apply the order of operations to reach a solution. Common Mistakes Made By Students Improper use of calculators: Students are usually very quick to use calculators when faced with formulas but if they are not proficient in using the order of operations, they will not insert parentheses where needed or press “=” at the wrong points and arrive at incorrect answers. Familiarity with the calculator: In some calculators, you must enter the radical sign first and in some calculators the radical sign is entered after the number is entered. Some calculators automatically do some of the correct order of operations. You need to know your calculator. Calculators are great tools, but you need to know the correct way to use them. When entering the square of a negative number in a calculator it is important to put it in parentheses. You need to enter (-2)^2 not - 22. For the latter the calculator thinks you are saying the negative of 2 squared or - 4 , and not (-2) (-2) = 4. When dealing with fractions students often will forget to put the numerator of the fraction and the denominator of the fraction in parentheses. If you enter (3 + 6)/9 into the scientific calculator, it recognizes that 3 + 6 is in the numerator and does this operation first, giving the answer 9/9 or 1. If you put 3 + 6/9 (without the parentheses) into a scientific calculator, it will give you an answer of 3.66… CTE Instructor’s Extended Discussion In the field of Marketing and Business, there are times when managers have to predict staffing and product needs to satisfy the marketing concept for the business they operate. The mathematical concept, Order of Operations, is a useful tool for managers to implement to help with this process. A manager who is able to evaluate and assess these variances in their daily operations can use this mathematical concept to help them predict how nature, labor, supply and demand will affect their business models. This can help the manager plan inventory and labor needs to keep the business operating in a profitable manner.

Problems Occupational (Contextual) Math Concepts Solutions

  1. Calculate the number of employees needed for concessions and parking at the park for a game: Where 1 employee is needed in concessions for every 20 tickets sold and 1 employee is needed in parking for 100 cars and on average there is 1 car for every two tickets sold. E = .05 b + .01(.5b) when b = 2000

E = 05(2000) +.01(.5(2000))

E = 100 + .01(1000)

E = 100 + 10

If 2000 tickets are sold, they need 110 employees to operate the concessions and parking for the game.

  1. Calculate the number of bottles of water needed if the temperature is 95 degrees and the number of presold tickets for the game is 3000. W = (.1(95 - 65))^2 x 1.05(3000) + W = (.1(30))^2 x 3150 + 500 W = (3)^2 x 3150 + 500 W = 9 x 3150 + 500 W = 28350 + 500 W = 28,
  2. There is a supply shortage of Coca-Cola®. A vendor needs to order Coca-Cola® for the weekend games. The amount of Coca-Cola the vendor is willing to supply is represented by the following formula: y= 2x^2 x = dollars/case and y= cases supplied How many cases is the supplier willing to deliver if the vendor is willing to pay $6.00/case? y= 2x^2 y= 2(6.00)^2 y= 2(36.00) y= 72 Problems Related, Generic Math Concepts Solutions
  3. Simplify 3 (5 + 7)^2 – 10/

3(5 +7)^2 – 10/5 =

3(12)^2 – 10/5 =

  1. Simplify 5(8 + 2) + (-5 + (2 + 3)(7 – 4))
  1. Simplify (5 + 8) 2 - (7 + 5) 2 (5 + 8)

Problems PA Core Math Look Solutions

  1. Simplify (5 + 7 + 3) ÷ (3 + 2) Following the order of operations, (5 + 7 + 3) ÷ (3 + 2) = Parenthesis 15 ÷ 5 = Division 3
  2. Simplify 5 + 7 + 3 ÷ 3 + 2 Following the order of operations, 5 + 7 + (3 ÷ 3) + 2 = Division 5 + 7 + 1 + 2 = Addition 15
  3. Compare problem #7 with problem #8. Explain how someone may make the mistake of thinking they are the same problem. In problem #7 you are asked to add 5 + 7 + 3 first, then add 3 + 2, and finally divide the two answers (5 + 7 + 3)/(3 + 2). In problem #8, the first thing to do is divide 3 by 3 and then add 5 + 7 + 1 + 2.