Math PPT
Applied Assignment #1
GBA 5212
Professor Smith
Algebra – The part of mathematics in which letters and other general symbols are used to represent numbers and quantities
“Because so many important business decisions are made on the basis of numbers, students need to learn how to analyze data and think critically about facts and figures” (Derrell, 2015)
Why Algebra?
Scenario
My company manufactures widgets that are sold on our website directly to the consumer. We’d like to learn what selling price makes us the most money. The relationship between the cost of an item and the quantity sold is linear (if we raise the price, the quantity sold will decrease).
Profit = total revenue – production costs. We can create a quadratic equation for this situation
The cost to produce each widget is $10
We will have to create a graph to find the slope for our slope-intercept equation Y = MX + B
| Selling Price $ (s) | Quantity Sold in 1 year (q) |
| $ 10.00 | 1000 |
| $ 15.00 | 900 |
| $ 20.00 | 800 |
| $ 25.00 | 700 |
From the graph we can conclude that our slope is -20 and our y-intercept will be at 1200
Quantity = q
Selling price = s
q = -20s +1200
Quantity Sold in 1 year (q) 10 15 20 25 1000 900 800 700
Profit Formula is P = sq - 10q
(profit = (selling price*quantity) – 10*quantity
10 is the cost to produce each widget
We will substitute -20s + 1200 for q in profit formula
P = s(-20s + 1200) – 10(-20s 1200)
P = -20s^2 + 1400s – 12000
We now have our quadratic equation
Quadratic Equation:
We can plug in selling price to the formula to evaluate which S is the most profitable with this equation
The selling price that generates the maximum profit is $15
Reflection:
Being able to develop and apply a quadratic equation for a business is extremely useful and does not take too long at all. It is very important that business’ recognize what volume/price relationship they need to obtain to maximum profits. Selling as much quantity as possible is not always a good thing for maximizing profits and can put an enormous amount of strain on personnel & equipment.
This will be helpful as I proceed into a management role in business to be able to find a sweet spot in pricing. This will also help me in my MBA when I am tasked with developing pricing strategies on projects.
Work Cited:
Derrell, Tracy. “Math Requirements for Business Majors.” AIUNIV.EDU, 2 Dec. 2015, www.aiuniv.edu/blog/2015/december/math-requirements.
Selling Price $ (s)Quantity Sold in 1 year (q)
10.00$ 100010,800.00$
15.00$ 90015,300.00$
20.00$ 8008,000.00$
25.00$ 70010,500.00$